A148514 - OEIS

A148514

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

1, 1, 3, 5, 17, 36, 134, 335, 1333, 3732, 15504, 46870, 200458, 640494, 2798585, 9330139, 41453055, 142971527, 643754048, 2282825370, 10391082024, 37709321557, 173189706730, 640888377597, 2965484008829, 11158376134888, 51957479350157, 198344225237265, 928535979959713, 3589580096542716

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OFFSET

0,3

LINKS

Table of n, a(n) for n=0..29.

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[-1 + i, j, k, -1 + n] + aux[1 + i, -1 + j, 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: A148511 A148512 A148513 * A105894 A305411 A019414

Adjacent sequences: A148511 A148512 A148513 * A148515 A148516 A148517

KEYWORD

nonn,walk

AUTHOR

Manuel Kauers, Nov 18 2008

STATUS

approved