A151172 - OEIS

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A151172

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

1, 3, 12, 49, 214, 946, 4304, 19727, 91830, 429586, 2028808, 9615266, 45859356, 219301044, 1053397024, 5070299771, 24485264294, 118436821842, 574327076360, 2788765754222, 13568119543636, 66085999862556, 322392161536992, 1574222913418742, 7696752549738556, 37661385553835476, 184479995723373904

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OFFSET

0,2

LINKS

Table of n, a(n) for n=0..26.

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[i, -1 + j, -1 + k, -1 + n] + aux[i, j, -1 + k, -1 + n] + aux[i, j, 1 + k, -1 + n] + aux[1 + i, 1 + 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: A052703 A151170 A151171 * A151173 A301456 A151174

Adjacent sequences: A151169 A151170 A151171 * A151173 A151174 A151175

KEYWORD

nonn,walk

AUTHOR

Manuel Kauers, Nov 18 2008

STATUS

approved