

A151394


Number of walks within N^2 (the first quadrant of Z^2) starting at (0,0), ending on the vertical axis and consisting of n steps taken from {(1, 1), (0, 1), (0, 1), (1, 1)}


0



1, 1, 2, 3, 8, 15, 44, 91, 286, 633, 2072, 4796, 16180, 38727, 133548, 327895, 1150226, 2881857, 10247072, 26099008, 93830568, 242264113, 878987980, 2295723288, 8393889812, 22139557300, 81484257064, 216757035756, 802324361696, 2150196732767, 7998562017700, 21576806128743, 80615634684738
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OFFSET

0,3


COMMENTS

Apparently a duplicate of A148005. [From R. J. Mathar, Dec 13 2008]


LINKS

Table of n, a(n) for n=0..32.
M. BousquetMelou and M. Mishna, 2008. Walks with small steps in the quarter plane, ArXiv 0810.4387.


MATHEMATICA

aux[i_Integer, j_Integer, n_Integer] := Which[Min[i, j, n] < 0  Max[i, j] > n, 0, n == 0, KroneckerDelta[i, j, n], True, aux[i, j, n] = aux[1 + i, 1 + j, 1 + n] + aux[i, 1 + j, 1 + n] + aux[i, 1 + j, 1 + n] + aux[1 + i, 1 + j, 1 + n]]; Table[Sum[aux[0, k, n], {k, 0, n}], {n, 0, 25}]


CROSSREFS

Sequence in context: A148004 A156802 A148005 * A148006 A148007 A148008
Adjacent sequences: A151391 A151392 A151393 * A151395 A151396 A151397


KEYWORD

nonn,walk


AUTHOR

Manuel Kauers, Nov 18 2008


STATUS

approved



