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TernaryTrees.tbl.md

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TernaryTrees

['A355172']

TernaryTrees Triangle view

Row Seq
Row0 [1]
Row1 [0, 1]
Row2 [0, 1, 3]
Row3 [0, 1, 5, 12]
Row4 [0, 1, 7, 25, 55]
Row5 [0, 1, 9, 42, 130, 273]
Row6 [0, 1, 11, 63, 245, 700, 1428]
Row7 [0, 1, 13, 88, 408, 1428, 3876, 7752]
Row8 [0, 1, 15, 117, 627, 2565, 8379, 21945, 43263]
Row9 [0, 1, 17, 150, 910, 4235, 15939, 49588, 126500, 246675]

TernaryTrees Triangles

Flat Seq
Triangle [[1], [0, 1], [0, 1, 3], [0, 1, 5, 12], [0, 1, 7, 25, 55], [0, 1, 9, 42, 130, 273], [0, 1, 11, 63, 245, 700, 1428], [0, 1, 13, 88, 408, 1428, 3876, 7752], [0, 1, 15, 117, 627, 2565, 8379, 21945, 43263], [0, 1, 17, 150, 910, 4235, 15939, 49588, 126500, 246675]]
RevTabl [[1], [1, 0], [3, 1, 0], [12, 5, 1, 0], [55, 25, 7, 1, 0], [273, 130, 42, 9, 1, 0], [1428, 700, 245, 63, 11, 1, 0], [7752, 3876, 1428, 408, 88, 13, 1, 0], [43263, 21945, 8379, 2565, 627, 117, 15, 1, 0], [246675, 126500, 49588, 15939, 4235, 910, 150, 17, 1, 0]]
AntiDiag [[1], [0], [0, 1], [0, 1], [0, 1, 3], [0, 1, 5], [0, 1, 7, 12], [0, 1, 9, 25], [0, 1, 11, 42, 55], [0, 1, 13, 63, 130]]
AccTabl [[1], [0, 1], [0, 1, 4], [0, 1, 6, 18], [0, 1, 8, 33, 88], [0, 1, 10, 52, 182, 455], [0, 1, 12, 75, 320, 1020, 2448], [0, 1, 14, 102, 510, 1938, 5814, 13566], [0, 1, 16, 133, 760, 3325, 11704, 33649, 76912], [0, 1, 18, 168, 1078, 5313, 21252, 70840, 197340, 444015]]
RevAccTabl [[1], [1, 0], [4, 1, 0], [18, 6, 1, 0], [88, 33, 8, 1, 0], [455, 182, 52, 10, 1, 0], [2448, 1020, 320, 75, 12, 1, 0], [13566, 5814, 1938, 510, 102, 14, 1, 0], [76912, 33649, 11704, 3325, 760, 133, 16, 1, 0], [444015, 197340, 70840, 21252, 5313, 1078, 168, 18, 1, 0]]
AccRevTabl [[1], [1, 1], [3, 4, 4], [12, 17, 18, 18], [55, 80, 87, 88, 88], [273, 403, 445, 454, 455, 455], [1428, 2128, 2373, 2436, 2447, 2448, 2448], [7752, 11628, 13056, 13464, 13552, 13565, 13566, 13566], [43263, 65208, 73587, 76152, 76779, 76896, 76911, 76912, 76912], [246675, 373175, 422763, 438702, 442937, 443847, 443997, 444014, 444015, 444015]]
DiffxTabl [[1], [0, 2], [0, 2, 9], [0, 2, 15, 48], [0, 2, 21, 100, 275], [0, 2, 27, 168, 650, 1638], [0, 2, 33, 252, 1225, 4200, 9996], [0, 2, 39, 352, 2040, 8568, 27132, 62016], [0, 2, 45, 468, 3135, 15390, 58653, 175560, 389367], [0, 2, 51, 600, 4550, 25410, 111573, 396704, 1138500, 2466750]]

TernaryTrees Row sums

Trait Seq
RowSum [1, 1, 4, 18, 88, 455, 2448, 13566, 76912, 444015]
EvenSum [1, 0, 3, 5, 62, 139, 1684, 4297, 52284, 143366]
OddSum [0, 1, 1, 13, 26, 316, 764, 9269, 24628, 300649]
AltSum [1, -1, 2, -8, 36, -177, 920, -4972, 27656, -157283]
AbsSum [1, 1, 4, 18, 88, 455, 2448, 13566, 76912, 444015]
AccSum [1, 1, 5, 25, 130, 700, 3876, 21945, 126500, 740025]
AccRevSum [1, 2, 11, 65, 398, 2485, 15708, 100149, 642620, 4144140]
DiagSum [1, 0, 1, 1, 4, 6, 20, 35, 109, 207]

TernaryTrees Transforms

Trans Seq
RowLcm [1, 1, 3, 60, 1925, 8190, 8246700, 7759752, 413377965, 135616981500]
RowGcd [1, 1, 3, 1, 1, 1, 1, 1, 3, 1]
RowMax [1, 1, 3, 12, 55, 273, 1428, 7752, 43263, 246675]
CentralE [1, 1, 7, 63, 627]
CentralO [0, 1, 9, 88, 910]
ColMiddle [1, 0, 1, 1, 7, 9, 63, 88, 627, 910]
ColLeft [1, 0, 0, 0, 0, 0, 0, 0, 0, 0]
ColRight [1, 1, 3, 12, 55, 273, 1428, 7752, 43263, 246675]
BinConv [1, 1, 5, 30, 201, 1438, 10734, 82512, 647945, 5170710]
InvBinConv [1, 1, 1, 0, -7, -42, -198, -858, -3575, -14586]
TransSqrs [0, 1, 13, 129, 1134, 9320, 73440, 562457, 4221052, 31202145]
TransNat0 [0, 1, 7, 47, 310, 2030, 13260, 86583, 565708, 3700125]
TransNat1 [1, 2, 11, 65, 398, 2485, 15708, 100149, 642620, 4144140]
PosHalf [1, 1, 5, 26, 141, 789, 4520, 26368, 156053, 934451]
NegHalf [1, 1, 1, 6, 25, 125, 648, 3504, 19489, 110835]

TernaryTrees Diagonals as rows

DiagRow Seq
DiagRow0 [1, 1, 3, 12, 55, 273, 1428, 7752, 43263, 246675]
DiagRow1 [0, 1, 5, 25, 130, 700, 3876, 21945, 126500, 740025]
DiagRow2 [0, 1, 7, 42, 245, 1428, 8379, 49588, 296010, 1781325]
DiagRow3 [0, 1, 9, 63, 408, 2565, 15939, 98670, 610740, 3786588]
DiagRow4 [0, 1, 11, 88, 627, 4235, 27830, 180180, 1157013, 7396972]
DiagRow5 [0, 1, 13, 117, 910, 6578, 45630, 308763, 2056912, 13564980]
DiagRow6 [0, 1, 15, 150, 1265, 9750, 71253, 503440, 3478200, 23662980]
DiagRow7 [0, 1, 17, 187, 1700, 13923, 106981, 788392, 5645904, 39617565]
DiagRow8 [0, 1, 19, 228, 2223, 19285, 155496, 1193808, 8855691, 64073529]
DiagRow9 [0, 1, 21, 273, 2842, 26040, 219912, 1756797, 13489164, 100591491]

TernaryTrees Diagonals as columns

DiagCol Seq
DiagCol0 [1, 0, 0, 0, 0, 0, 0, 0, 0, 0]
DiagCol1 [1, 1, 1, 1, 1, 1, 1, 1, 1, 1]
DiagCol2 [3, 5, 7, 9, 11, 13, 15, 17, 19, 21]
DiagCol3 [12, 25, 42, 63, 88, 117, 150, 187, 228, 273]
DiagCol4 [55, 130, 245, 408, 627, 910, 1265, 1700, 2223, 2842]
DiagCol5 [273, 700, 1428, 2565, 4235, 6578, 9750, 13923, 19285, 26040]
DiagCol6 [1428, 3876, 8379, 15939, 27830, 45630, 71253, 106981, 155496, 219912]
DiagCol7 [7752, 21945, 49588, 98670, 180180, 308763, 503440, 788392, 1193808, 1756797]
DiagCol8 [43263, 126500, 296010, 610740, 1157013, 2056912, 3478200, 5645904, 8855691, 13489164]
DiagCol9 [246675, 740025, 1781325, 3786588, 7396972, 13564980, 23662980, 39617565, 64073529, 100591491]

TernaryTrees Polynomial values as rows

PolyRow Seq
PolyRow0 [1, 1, 1, 1, 1, 1, 1, 1, 1, 1]
PolyRow1 [0, 1, 2, 3, 4, 5, 6, 7, 8, 9]
PolyRow2 [0, 4, 14, 30, 52, 80, 114, 154, 200, 252]
PolyRow3 [0, 18, 118, 372, 852, 1630, 2778, 4368, 6472, 9162]
PolyRow4 [0, 88, 1110, 5196, 15796, 37680, 76938, 140980, 238536, 379656]
PolyRow5 [0, 455, 11190, 78087, 315668, 939855, 2300730, 4915295, 9500232, 17004663]
PolyRow6 [0, 2448, 118262, 1232760, 6632820, 24661280, 72399498, 180378072, 398315720, 801886320]
PolyRow7 [0, 13566, 1293302, 20161776, 144457428, 670916330, 2362554906, 6865123692, 17321702216, 39224505078]
PolyRow8 [0, 76912, 14513654, 338627928, 3231946036, 18753406880, 79220137002, 268505674024, 774137880008, 1971901150416]
PolyRow9 [0, 444015, 166200310, 5806446033, 73836990612, 535338103555, 2713046344890, 10726259805765, 35338790342728, 101258263989207]

TernaryTrees Polynomial values as columns

PolyCol Seq
PolyCol0 [1, 0, 0, 0, 0, 0, 0, 0, 0, 0]
PolyCol1 [1, 1, 4, 18, 88, 455, 2448, 13566, 76912, 444015]
PolyCol2 [1, 2, 14, 118, 1110, 11190, 118262, 1293302, 14513654, 166200310]
PolyCol3 [1, 3, 30, 372, 5196, 78087, 1232760, 20161776, 338627928, 5806446033]
PolyCol4 [1, 4, 52, 852, 15796, 315668, 6632820, 144457428, 3231946036, 73836990612]
PolyCol5 [1, 5, 80, 1630, 37680, 939855, 24661280, 670916330, 18753406880, 535338103555]
PolyCol6 [1, 6, 114, 2778, 76938, 2300730, 72399498, 2362554906, 79220137002, 2713046344890]
PolyCol7 [1, 7, 154, 4368, 140980, 4915295, 180378072, 6865123692, 268505674024, 10726259805765]
PolyCol8 [1, 8, 200, 6472, 238536, 9500232, 398315720, 17321702216, 774137880008, 35338790342728]
PolyCol9 [1, 9, 252, 9162, 379656, 17004663, 801886320, 39224505078, 1971901150416, 101258263989207]

TernaryTrees:Rev

[]

TernaryTrees:Rev Triangle view

Row Seq
Row0 [1]
Row1 [1, 0]
Row2 [3, 1, 0]
Row3 [12, 5, 1, 0]
Row4 [55, 25, 7, 1, 0]
Row5 [273, 130, 42, 9, 1, 0]
Row6 [1428, 700, 245, 63, 11, 1, 0]
Row7 [7752, 3876, 1428, 408, 88, 13, 1, 0]
Row8 [43263, 21945, 8379, 2565, 627, 117, 15, 1, 0]
Row9 [246675, 126500, 49588, 15939, 4235, 910, 150, 17, 1, 0]

TernaryTrees:Rev Triangles

Flat Seq
Triangle [[1], [1, 0], [3, 1, 0], [12, 5, 1, 0], [55, 25, 7, 1, 0], [273, 130, 42, 9, 1, 0], [1428, 700, 245, 63, 11, 1, 0], [7752, 3876, 1428, 408, 88, 13, 1, 0], [43263, 21945, 8379, 2565, 627, 117, 15, 1, 0], [246675, 126500, 49588, 15939, 4235, 910, 150, 17, 1, 0]]
RevTabl [[1], [0, 1], [0, 1, 3], [0, 1, 5, 12], [0, 1, 7, 25, 55], [0, 1, 9, 42, 130, 273], [0, 1, 11, 63, 245, 700, 1428], [0, 1, 13, 88, 408, 1428, 3876, 7752], [0, 1, 15, 117, 627, 2565, 8379, 21945, 43263], [0, 1, 17, 150, 910, 4235, 15939, 49588, 126500, 246675]]
AntiDiag [[1], [1], [3, 0], [12, 1], [55, 5, 0], [273, 25, 1], [1428, 130, 7, 0], [7752, 700, 42, 1], [43263, 3876, 245, 9, 0], [246675, 21945, 1428, 63, 1]]
AccTabl [[1], [1, 1], [3, 4, 4], [12, 17, 18, 18], [55, 80, 87, 88, 88], [273, 403, 445, 454, 455, 455], [1428, 2128, 2373, 2436, 2447, 2448, 2448], [7752, 11628, 13056, 13464, 13552, 13565, 13566, 13566], [43263, 65208, 73587, 76152, 76779, 76896, 76911, 76912, 76912], [246675, 373175, 422763, 438702, 442937, 443847, 443997, 444014, 444015, 444015]]
RevAccTabl [[1], [1, 1], [4, 4, 3], [18, 18, 17, 12], [88, 88, 87, 80, 55], [455, 455, 454, 445, 403, 273], [2448, 2448, 2447, 2436, 2373, 2128, 1428], [13566, 13566, 13565, 13552, 13464, 13056, 11628, 7752], [76912, 76912, 76911, 76896, 76779, 76152, 73587, 65208, 43263], [444015, 444015, 444014, 443997, 443847, 442937, 438702, 422763, 373175, 246675]]
AccRevTabl [[1], [0, 1], [0, 1, 4], [0, 1, 6, 18], [0, 1, 8, 33, 88], [0, 1, 10, 52, 182, 455], [0, 1, 12, 75, 320, 1020, 2448], [0, 1, 14, 102, 510, 1938, 5814, 13566], [0, 1, 16, 133, 760, 3325, 11704, 33649, 76912], [0, 1, 18, 168, 1078, 5313, 21252, 70840, 197340, 444015]]
DiffxTabl [[1], [1, 0], [3, 2, 0], [12, 10, 3, 0], [55, 50, 21, 4, 0], [273, 260, 126, 36, 5, 0], [1428, 1400, 735, 252, 55, 6, 0], [7752, 7752, 4284, 1632, 440, 78, 7, 0], [43263, 43890, 25137, 10260, 3135, 702, 105, 8, 0], [246675, 253000, 148764, 63756, 21175, 5460, 1050, 136, 9, 0]]

TernaryTrees:Rev Row sums

Trait Seq
RowSum [1, 1, 4, 18, 88, 455, 2448, 13566, 76912, 444015]
EvenSum [1, 1, 3, 13, 62, 316, 1684, 9269, 52284, 300649]
OddSum [0, 0, 1, 5, 26, 139, 764, 4297, 24628, 143366]
AltSum [1, 1, 2, 8, 36, 177, 920, 4972, 27656, 157283]
AbsSum [1, 1, 4, 18, 88, 455, 2448, 13566, 76912, 444015]
AccSum [1, 2, 11, 65, 398, 2485, 15708, 100149, 642620, 4144140]
AccRevSum [1, 1, 5, 25, 130, 700, 3876, 21945, 126500, 740025]
DiagSum [1, 1, 3, 13, 60, 299, 1565, 8495, 47393, 270112]

TernaryTrees:Rev Transforms

Trans Seq
RowLcm [1, 1, 3, 60, 1925, 8190, 8246700, 7759752, 413377965, 135616981500]
RowGcd [1, 1, 3, 1, 1, 1, 1, 1, 3, 1]
RowMax [1, 1, 3, 12, 55, 273, 1428, 7752, 43263, 246675]
CentralE [1, 1, 7, 63, 627]
CentralO [1, 5, 42, 408, 4235]
ColMiddle [1, 1, 1, 5, 7, 42, 63, 408, 627, 4235]
ColLeft [1, 1, 3, 12, 55, 273, 1428, 7752, 43263, 246675]
ColRight [1, 0, 0, 0, 0, 0, 0, 0, 0, 0]
BinConv [1, 1, 5, 30, 201, 1438, 10734, 82512, 647945, 5170710]
InvBinConv [1, -1, 1, 0, -7, 42, -198, 858, -3575, 14586]
TransSqrs [0, 0, 1, 9, 62, 395, 2448, 15029, 92092, 565110]
TransNat0 [0, 0, 1, 7, 42, 245, 1428, 8379, 49588, 296010]
TransNat1 [1, 1, 5, 25, 130, 700, 3876, 21945, 126500, 740025]
PosHalf [1, 2, 14, 118, 1110, 11190, 118262, 1293302, 14513654, 166200310]
NegHalf [1, -2, 10, -78, 706, -6958, 72450, -784014, 8729698, -99362862]

TernaryTrees:Rev Diagonals as rows

DiagRow Seq
DiagRow0 [1, 0, 0, 0, 0, 0, 0, 0, 0, 0]
DiagRow1 [1, 1, 1, 1, 1, 1, 1, 1, 1, 1]
DiagRow2 [3, 5, 7, 9, 11, 13, 15, 17, 19, 21]
DiagRow3 [12, 25, 42, 63, 88, 117, 150, 187, 228, 273]
DiagRow4 [55, 130, 245, 408, 627, 910, 1265, 1700, 2223, 2842]
DiagRow5 [273, 700, 1428, 2565, 4235, 6578, 9750, 13923, 19285, 26040]
DiagRow6 [1428, 3876, 8379, 15939, 27830, 45630, 71253, 106981, 155496, 219912]
DiagRow7 [7752, 21945, 49588, 98670, 180180, 308763, 503440, 788392, 1193808, 1756797]
DiagRow8 [43263, 126500, 296010, 610740, 1157013, 2056912, 3478200, 5645904, 8855691, 13489164]
DiagRow9 [246675, 740025, 1781325, 3786588, 7396972, 13564980, 23662980, 39617565, 64073529, 100591491]

TernaryTrees:Rev Diagonals as columns

DiagCol Seq
DiagCol0 [1, 1, 3, 12, 55, 273, 1428, 7752, 43263, 246675]
DiagCol1 [0, 1, 5, 25, 130, 700, 3876, 21945, 126500, 740025]
DiagCol2 [0, 1, 7, 42, 245, 1428, 8379, 49588, 296010, 1781325]
DiagCol3 [0, 1, 9, 63, 408, 2565, 15939, 98670, 610740, 3786588]
DiagCol4 [0, 1, 11, 88, 627, 4235, 27830, 180180, 1157013, 7396972]
DiagCol5 [0, 1, 13, 117, 910, 6578, 45630, 308763, 2056912, 13564980]
DiagCol6 [0, 1, 15, 150, 1265, 9750, 71253, 503440, 3478200, 23662980]
DiagCol7 [0, 1, 17, 187, 1700, 13923, 106981, 788392, 5645904, 39617565]
DiagCol8 [0, 1, 19, 228, 2223, 19285, 155496, 1193808, 8855691, 64073529]
DiagCol9 [0, 1, 21, 273, 2842, 26040, 219912, 1756797, 13489164, 100591491]

TernaryTrees:Rev Polynomial values as rows

PolyRow Seq
PolyRow0 [1, 1, 1, 1, 1, 1, 1, 1, 1, 1]
PolyRow1 [1, 1, 1, 1, 1, 1, 1, 1, 1, 1]
PolyRow2 [3, 4, 5, 6, 7, 8, 9, 10, 11, 12]
PolyRow3 [12, 18, 26, 36, 48, 62, 78, 96, 116, 138]
PolyRow4 [55, 88, 141, 220, 331, 480, 673, 916, 1215, 1576]
PolyRow5 [273, 455, 789, 1365, 2297, 3723, 5805, 8729, 12705, 17967]
PolyRow6 [1428, 2448, 4520, 8568, 16020, 28928, 50088, 83160, 132788, 204720]
PolyRow7 [7752, 13566, 26368, 54264, 112152, 225082, 432336, 792228, 1387624, 2332182]
PolyRow8 [43263, 76912, 156053, 346104, 787411, 1753088, 3732777, 7547368, 14499719, 26566416]
PolyRow9 [246675, 444015, 934451, 2220075, 5540643, 13664375, 32235315, 71904051, 151508915, 302615103]

TernaryTrees:Rev Polynomial values as columns

PolyCol Seq
PolyCol0 [1, 1, 3, 12, 55, 273, 1428, 7752, 43263, 246675]
PolyCol1 [1, 1, 4, 18, 88, 455, 2448, 13566, 76912, 444015]
PolyCol2 [1, 1, 5, 26, 141, 789, 4520, 26368, 156053, 934451]
PolyCol3 [1, 1, 6, 36, 220, 1365, 8568, 54264, 346104, 2220075]
PolyCol4 [1, 1, 7, 48, 331, 2297, 16020, 112152, 787411, 5540643]
PolyCol5 [1, 1, 8, 62, 480, 3723, 28928, 225082, 1753088, 13664375]
PolyCol6 [1, 1, 9, 78, 673, 5805, 50088, 432336, 3732777, 32235315]
PolyCol7 [1, 1, 10, 96, 916, 8729, 83160, 792228, 7547368, 71904051]
PolyCol8 [1, 1, 11, 116, 1215, 12705, 132788, 1387624, 14499719, 151508915]
PolyCol9 [1, 1, 12, 138, 1576, 17967, 204720, 2332182, 26566416, 302615103]