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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.
2
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
1,4
FORMULA
A(n,k) = (1 + (3^n - 2^(n + 1))*(6*k - 3 + 2*(-1)^n))/6, n,k >= 1.
EXAMPLE
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
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}]]
CROSSREFS
Sequence in context: A368204 A318166 A241845 * A339014 A175910 A257662
KEYWORD
sign,tabl
AUTHOR
L. Edson Jeffery, May 03 2015
STATUS
approved