A149491 - OEIS

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A149491

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

1, 1, 4, 14, 56, 237, 1036, 4603, 20951, 96544, 448844, 2106027, 9950648, 47254566, 225457864, 1080095458, 5191016887, 25019333735, 120895386015, 585447565802, 2840483620046, 13805374592905, 67200268124866, 327556541371822, 1598606372758210, 7810659910922604, 38201283093553175, 187014395949907268

(list; graph; refs; listen; history; text; internal format)

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, -1 + j, 1 + k, -1 + n] + aux[i, 1 + j, -1 + k, -1 + n] + aux[1 + i, -1 + j, -1 + k, -1 + n] + aux[1 + i, 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: A323787 A132837 A259808 * A073155 A365114 A370720

Adjacent sequences: A149488 A149489 A149490 * A149492 A149493 A149494

KEYWORD

nonn,walk

AUTHOR

Manuel Kauers, Nov 18 2008

STATUS

approved