A151285 - OEIS

A151285

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

1, 2, 6, 20, 70, 257, 967, 3722, 14548, 57619, 230612, 931083, 3787276, 15502881, 63810147, 263909613, 1096140669, 4570019368, 19117859437, 80220313298, 337542496835, 1423849191982, 6020011578673, 25506250066482, 108277897776181, 460482597553895, 1961598838029100, 8369127049893122

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OFFSET

0,2

LINKS

Table of n, a(n) for n=0..27.

M. Bousquet-Mélou and M. Mishna, 2008. Walks with small steps in the quarter plane, ArXiv 0810.4387.

A. Bostan and M. Kauers, 2008. Automatic Classification of Restricted Lattice Walks, ArXiv 0811.2899.

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[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[Sum[aux[i, j, n], {i, 0, n}, {j, 0, n}], {n, 0, 25}]

CROSSREFS

Sequence in context: A049140 A372526 A092413 * A150126 A150127 A151286

Adjacent sequences: A151282 A151283 A151284 * A151286 A151287 A151288

KEYWORD

nonn,walk

AUTHOR

Manuel Kauers, Nov 18 2008

STATUS

approved