

A151498


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


0



1, 1, 3, 12, 57, 301, 1707, 10191, 63244, 404503, 2650293, 17709684, 120288313, 828352036, 5771747783, 40625485570, 288482116987, 2064429518054, 14874855533504, 107832596542894, 785986247826371, 5757192302807027, 42357833323697589, 312901369167191854, 2319946973815289676
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OFFSET

0,3


LINKS

Table of n, a(n) for n=0..24.
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, j, 1 + n] + aux[1 + i, 1 + j, 1 + n] + aux[1 + i, 1 + j, 1 + n]]; Table[Sum[aux[0, k, 2 n], {k, 0, 2 n}], {n, 0, 25}]


CROSSREFS

Sequence in context: A178807 A047891 A166991 * A103370 A094149 A117107
Adjacent sequences: A151495 A151496 A151497 * A151499 A151500 A151501


KEYWORD

nonn,walk


AUTHOR

Manuel Kauers, Nov 18 2008


STATUS

approved



