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

1,2

Comments

Sequence is a permutation of the natural numbers.

Is this array the same as the dispersion A191668?

Links

Table of n, a(n) for n=1..55.

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.

Example

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.

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}]]

Crossrefs

Cf. A000302, A042965, A016825, A191668.

Sequence in context: A084793 A033820 A095259 * A265353 A266189 A371635

Adjacent sequences: A260593 A260594 A260595 * A260597 A260598 A260599

Keyword

nonn,tabl

Author

L. Edson Jeffery, Jul 29 2015

Extensions

Edited: Wolfdieter Lang, Aug 16 2015

Status

approved