A148864 - OEIS

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A148864

Number of walks within N^3 (the first octant of Z^3) starting at (0,0,0) and consisting of n steps taken from {(-1, 0, 0), (0, -1, 1), (0, 0, 1), (1, 0, -1), (1, 1, -1)}.

1, 1, 3, 8, 28, 96, 360, 1384, 5513, 22356, 92884, 391014, 1669886, 7215742, 31490654, 138607154, 615048548, 2747302204, 12346906738, 55802001785, 253432831954, 1156167541210, 5296570959500, 24354455083955, 112371278895130, 520151980622491, 2414733832563686, 11240552129122354, 52458510164088043

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OFFSET

0,3

LINKS

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

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

MATHEMATICA

aux[i_Integer, j_Integer, k_Integer, n_Integer] := Which[Min[i, j, k, n] < 0 || Max[i, j, k] > n, 0, n == 0, KroneckerDelta[i, j, k, n], True, aux[i, j, k, n] = aux[-1 + i, -1 + j, 1 + k, -1 + n] + aux[-1 + i, j, 1 + k, -1 + n] + aux[i, j, -1 + k, -1 + n] + aux[i, 1 + j, -1 + k, -1 + n] + aux[1 + i, j, k, -1 + n]]; Table[Sum[aux[i, j, k, n], {i, 0, n}, {j, 0, n}, {k, 0, n}], {n, 0, 10}]

CROSSREFS

Sequence in context: A148861 A148862 A148863 * A148865 A203152 A362645

Adjacent sequences: A148861 A148862 A148863 * A148865 A148866 A148867

KEYWORD

nonn,walk

AUTHOR

Manuel Kauers, Nov 18 2008

STATUS

approved