A149376 - OEIS

A149376

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

1, 1, 4, 12, 48, 165, 711, 2765, 12230, 50199, 227229, 970714, 4459345, 19565405, 90903964, 406827818, 1906585122, 8662077597, 40874264328, 187908308360, 891647946915, 4138130214503, 19726740618496, 92263851819229, 441537841755276, 2078452663508263, 9979603884251570, 47232397814709432

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OFFSET

0,3

LINKS

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

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, k, -1 + n] + aux[-1 + i, j, 1 + k, -1 + n] + aux[-1 + i, 1 + j, k, -1 + n] + aux[1 + i, 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: A262414 A081620 A282023 * A149377 A063887 A149378

Adjacent sequences: A149373 A149374 A149375 * A149377 A149378 A149379

KEYWORD

nonn,walk

AUTHOR

Manuel Kauers, Nov 18 2008

STATUS

approved