A148313 - OEIS

A148313

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

1, 1, 2, 5, 14, 37, 116, 370, 1183, 3971, 13722, 47242, 167992, 601874, 2180993, 7999405, 29583543, 110326116, 414785272, 1568477396, 5972561563, 22861229453, 87965677392, 340135974318, 1320732933038, 5149935600016, 20158068763761, 79173030560182, 312031889479505, 1233497653080074, 4890367886626666

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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, 1 + j, 1 + k, -1 + n] + aux[i, -1 + j, -1 + k, -1 + n] + aux[1 + i, -1 + j, k, -1 + n] + aux[1 + i, j, -1 + 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: A148310 A148311 A148312 * A228952 A172259 A292327

Adjacent sequences: A148310 A148311 A148312 * A148314 A148315 A148316

KEYWORD

nonn,walk

AUTHOR

Manuel Kauers, Nov 18 2008

STATUS

approved