A149334 - OEIS

A149334

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

1, 1, 4, 12, 40, 145, 543, 2073, 8121, 32419, 131221, 537789, 2227180, 9308051, 39212347, 166345346, 710026110, 3047504428, 13145873941, 56963607057, 247851047180, 1082474012820, 4744026983562, 20857543773642, 91973169330527, 406676592174095, 1802793008076923, 8010846458934011

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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[i, 1 + 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: A074032 A074450 A028403 * A149335 A149336 A149337

Adjacent sequences: A149331 A149332 A149333 * A149335 A149336 A149337

KEYWORD

nonn,walk

AUTHOR

Manuel Kauers, Nov 18 2008

STATUS

approved