A151405 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, 0), (0, -1), (0, 1), (1, 1)}.

1, 1, 3, 8, 23, 75, 238, 800, 2734, 9417, 33207, 117661, 421563, 1524047, 5537482, 20269868, 74545781, 275422975, 1022213776, 3806863892, 14227928563, 53338307668, 200505927183, 755722398596, 2854949775551, 10808994805493, 41006118620478, 155852743565206, 593389348239315, 2262898414661276

Offset

0,3

Links

Table of n, a(n) for n=0..29.

M. Bousquet-Mélou 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, j, -1 + n]]; Table[Sum[aux[0, k, n], {k, 0, n}], {n, 0, 25}]

Crossrefs

Sequence in context: A101495 A134758 A050511 * A148778 A099265 A099266

Adjacent sequences: A151402 A151403 A151404 * A151406 A151407 A151408

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved