A151262 - OEIS

A151262

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

1, 1, 3, 6, 18, 47, 141, 416, 1278, 3983, 12616, 40475, 131461, 430548, 1423924, 4741118, 15896509, 53622384, 181826538, 619678461, 2121171010, 7290531452, 25152947775, 87076167883, 302422286268, 1053449686642, 3679700846025, 12886585101117, 45238465102771, 159171202374935, 561236984775150, 1982888741975501

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OFFSET

0,3

LINKS

Table of n, a(n) for n=0..31.

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

CROSSREFS

Sequence in context: A223044 A317078 A289587 * A148555 A148556 A148557

Adjacent sequences: A151259 A151260 A151261 * A151263 A151264 A151265

KEYWORD

nonn,walk

AUTHOR

Manuel Kauers, Nov 18 2008

STATUS

approved