A148502 - OEIS

A148502

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

1, 1, 3, 5, 15, 33, 119, 307, 1145, 3121, 11951, 35141, 139831, 427607, 1714441, 5420309, 22183715, 72324439, 298824829, 993349021, 4142872043, 14065088951, 59209316301, 204041427767, 863673823849, 3018732122265, 12867879154311, 45529390221089, 194959475597363, 696922326292943, 2998774832112917

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OFFSET

0,3

LINKS

Table of n, a(n) for n=0..30.

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, j, 1 + k, -1 + n] + aux[i, -1 + j, 1 + k, -1 + n] + aux[i, j, -1 + k, -1 + n] + aux[1 + i, 1 + j, -1 + k, -1 + n] + aux[1 + i, 1 + j, 1 + 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: A148499 A148500 A148501 * A295614 A089485 A279684

Adjacent sequences: A148499 A148500 A148501 * A148503 A148504 A148505

KEYWORD

nonn,walk

AUTHOR

Manuel Kauers, Nov 18 2008

STATUS

approved