A151018 - OEIS

A151018

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

1, 2, 9, 39, 189, 896, 4417, 21576, 107073, 529240, 2634775, 13093073, 65293025, 325328452, 1623926483, 8102847121, 40470054325, 202092673302, 1009726970717, 5044555157671, 25210265604259, 125984999325888, 629709173954791, 3147443384782430, 15733446109267457, 78648558624960914

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OFFSET

0,2

LINKS

Table of n, a(n) for n=0..25.

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, -1 + j, 1 + 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]]; Table[Sum[aux[i, j, k, n], {i, 0, n}, {j, 0, n}, {k, 0, n}], {n, 0, 10}]

CROSSREFS

Sequence in context: A151015 A151016 A151017 * A096359 A020002 A346687

Adjacent sequences: A151015 A151016 A151017 * A151019 A151020 A151021

KEYWORD

nonn,walk

AUTHOR

Manuel Kauers, Nov 18 2008

STATUS

approved