

A151503


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), (1, 1), (1, 0)}


0



1, 0, 1, 1, 3, 6, 17, 40, 117, 314, 912, 2667, 7916, 23963, 73586, 227611, 715444, 2262450, 7223397, 23261164, 75343490, 245847919, 806839587, 2661738663, 8829581024, 29418789715, 98457806482, 330890849398, 1116135299721, 3778754481148, 12835824454442, 43738283921029, 149490351563243, 512353843888497
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OFFSET

0,5


LINKS

M. BousquetMélou 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[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



KEYWORD

nonn,walk


AUTHOR



STATUS

approved



