A149972 - OEIS

A149972

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

1, 2, 5, 16, 55, 206, 805, 3242, 13477, 57053, 246156, 1077655, 4773424, 21378709, 96572231, 439708996, 2015776682, 9295605228, 43098363308, 200758507109, 939156465191, 4410267037286, 20781857902622, 98236710962403, 465694144735972, 2213421845801600, 10545568951022335, 50353797778192495

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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[-1 + i, j, 1 + k, -1 + n] + aux[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: A157418 A149971 A176828 * A026106 A308027 A066642

Adjacent sequences: A149969 A149970 A149971 * A149973 A149974 A149975

KEYWORD

nonn,walk

AUTHOR

Manuel Kauers, Nov 18 2008

STATUS

approved