A151032 - OEIS

A151032

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

1, 3, 9, 29, 105, 401, 1565, 6235, 25435, 105201, 440165, 1861067, 7942453, 34118021, 147539839, 641724317, 2805400805, 12314901173, 54284939599, 240146460337, 1065873647065, 4744406887317, 21177750028993, 94762922039031, 425024963073671, 1910295056145189, 8603324765426951, 38816474157873677

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OFFSET

0,2

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, j, k, -1 + n] + aux[i, -1 + j, k, -1 + n] + aux[i, j, -1 + k, -1 + n] + aux[1 + 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: A177255 A136628 A151031 * A007472 A292756 A151451

Adjacent sequences: A151029 A151030 A151031 * A151033 A151034 A151035

KEYWORD

nonn,walk

AUTHOR

Manuel Kauers, Nov 18 2008

STATUS

approved