A148555 - OEIS

A148555

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

1, 1, 3, 6, 18, 47, 141, 432, 1329, 4452, 14295, 49817, 167179, 591475, 2062501, 7357786, 26446105, 95239479, 349688079, 1274422929, 4742103229, 17511528513, 65687166495, 245724681207, 926977717315, 3507504480858, 13301679890417, 50792123226168, 193720256273361, 744703358194793, 2857772882473509

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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, k, -1 + n] + aux[i, -1 + j, 1 + k, -1 + n] + aux[1 + i, 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: A317078 A289587 A151262 * A148556 A148557 A148558

Adjacent sequences: A148552 A148553 A148554 * A148556 A148557 A148558

KEYWORD

nonn,walk

AUTHOR

Manuel Kauers, Nov 18 2008

STATUS

approved