A254131 Rectangular array A read by upward antidiagonals in which the entry in row n and column k is defined by A(n,k) = A254067(n,k) - A257499(n,k), n,k >= 1.

0, 1, -1, 2, 2, -2, 41, 13, 3, -3, 30, 90, 24, 4, -4, 501, 209, 139, 35, 5, -5, 322, 1102, 388, 188, 46, 6, -6, 5041, 2253, 1703, 567, 237, 57, 7, -7, 3110, 11090, 4184, 2304, 746, 286, 68, 8, -8, 47501, 21769, 17139, 6115, 2905, 925, 335, 79, 9, -9

Offset: 1

Author

L. Edson Jeffery, May 03 2015

Keywords

• sign
• tabl

Examples

			A begins:
.       0     -1     -2     -3     -4     -5     -6     -7     -8     -9
.       1      2      3      4      5      6      7      8      9     10
.       2     13     24     35     46     57     68     79     90    101
.      41     90    139    188    237    286    335    384    433    482
.      30    209    388    567    746    925   1104   1283   1462   1641
.     501   1102   1703   2304   2905   3506   4107   4708   5309   5910
.     322   2253   4184   6115   8046   9977  11908  13839  15770  17701
.    5041  11090  17139  23188  29237  35286  41335  47384  53433  59482
.    3110  21769  40428  59087  77746  96405 115064 133723 152382 171041
.   47501 104502 161503 218504 275505 332506 389507 446508 503509 560510
		

Programs

Mathematica

(* Array: *)
A254131[n_, k_] := (1 + (3^n - 2^(n + 1))*(6*k - 3 + 2*(-1)^n))/6; Grid[Table[A254131[n, k], {n, 10}, {k, 10}]]
(* Array antidiagonals flattened: *)
Flatten[Table[(1 + (3^(n - k + 1) - 2^(n - k + 2))*(6*k - 3 + 2*(-1)^(n - k + 1)))/6, {n, 10}, {k, n}]]

Formula

A(n,k) = (1 + (3^n - 2^(n + 1))*(6*k - 3 + 2*(-1)^n))/6, n,k >= 1.