A148421 - OEIS

A148421

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

1, 1, 2, 5, 18, 57, 198, 717, 2756, 10529, 41553, 167333, 683317, 2810043, 11743208, 49541544, 210275241, 899164766, 3877972563, 16807996275, 73177208572, 320397904631, 1409529888750, 6221283876244, 27560583227947, 122569219642023, 546712751707494, 2444905375175623, 10965472658203978

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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[i, -1 + j, k, -1 + n] + aux[i, -1 + j, 1 + k, -1 + n] + aux[1 + i, j, 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: A148418 A148419 A148420 * A148422 A148423 A148424

Adjacent sequences: A148418 A148419 A148420 * A148422 A148423 A148424

KEYWORD

nonn,walk

AUTHOR

Manuel Kauers, Nov 18 2008

STATUS

approved