A151358 Number of walks within N^2 (the first quadrant of Z^2) starting and ending at (0,0) and consisting of n steps taken from {(-1, -1), (-1, 0), (-1, 1), (0, 1), (1, -1), (1, 0)}.

1, 0, 1, 3, 7, 29, 101, 404, 1657, 6987, 30666, 136679, 624485, 2899186, 13670079, 65344840, 316012215, 1544872132, 7624022772, 37951505458, 190398999412, 962031788591, 4892669207705, 25032214282235, 128780148586223, 665906668042143, 3459650667634130, 18053515979281908, 94595985460340024

Offset

0,4

Links

Table of n, a(n) for n=0..28.

A. Bostan, K. Raschel, B. Salvy, Non-D-finite excursions in the quarter plane, J. Comb. Theory A 121 (2014) 45-63, Table 1 Tag 47, Tag 51

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, j, -1 + n] + aux[-1 + i, 1 + j, -1 + n] + aux[i, -1 + j, -1 + n] + aux[1 + i, -1 + j, -1 + n] + aux[1 + i, j, -1 + n] + aux[1 + i, 1 + j, -1 + n]]; Table[aux[0, 0, n], {n, 0, 25}]

Crossrefs

Sequence in context: A148766 A148767 A171180 * A110613 A337489 A363208

Adjacent sequences: A151355 A151356 A151357 * A151359 A151360 A151361

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved