A260596 Array A read by upward antidiagonals in which the entry A(n,k) in row n and column k is defined by A(n,k) = (8 + (3*floor((4*n + 1)/3) - 2)*4^k)/12, n,k >= 1.
1, 3, 2, 4, 10, 6, 5, 14, 38, 22, 7, 18, 54, 150, 86, 8, 26, 70, 214, 598, 342, 9, 30, 102, 278, 854, 2390, 1366, 11, 34, 118, 406, 1110, 3414, 9558, 5462, 12, 42, 134, 470, 1622, 4438, 13654, 38230, 21846, 13, 46, 166, 534, 1878, 6486, 17750, 54614, 152918, 87382
Offset: 1
Examples
Array A begins: . 1 2 6 22 86 342 1366 5462 21846 87382 . 3 10 38 150 598 2390 9558 38230 152918 611670 . 4 14 54 214 854 3414 13654 54614 218454 873814 . 5 18 70 278 1110 4438 17750 70998 283990 1135958 . 7 26 102 406 1622 6486 25942 103766 415062 1660246 . 8 30 118 470 1878 7510 30038 120150 480598 1922390 . 9 34 134 534 2134 8534 34134 136534 546134 2184534 . 11 42 166 662 2646 10582 42326 169302 677206 2708822 . 12 46 182 726 2902 11606 46422 185686 742742 2970966 . 13 50 198 790 3158 12630 50518 202070 808278 3233110 ... The triangle T(n, k) begins: n\k 1 2 3 4 5 6 7 8 9 10 ... 1: 1 2: 3 2 3: 4 10 6 4: 5 14 38 22 5: 7 18 54 150 86 6: 8 26 70 214 598 342 7: 9 30 102 278 854 2390 1366 8: 11 34 118 406 1110 3414 9558 5462 9: 12 42 134 470 1622 4438 13654 38230 21846 10:13 46 166 534 1878 6486 17750 54614 152918 87382 ... Triangle formatted by _Wolfdieter Lang_, Aug 16 2015.
Programs
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Mathematica
(* Array: *) Grid[Table[(8 + (3*Floor[(4*n + 1)/3] - 2)*4^k)/12, {n, 10}, {k, 10}]] (* Array antidiagonals flattened: *) Flatten[Table[(8 + (3*Floor[(4*(n - k) + 5)/3] - 2)*4^k)/12, {n, 10}, {k, n}]]
Formula
T(n,k) = A(n-k+1,k) = (8 + (3*floor((4*(n-k+1) + 1)/3) - 2)*4^k)/12, n >= k >=1.
Extensions
Edited: Wolfdieter Lang, Aug 16 2015
Comments