A148163 - OEIS

A148163

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

1, 1, 2, 4, 11, 31, 91, 283, 901, 2904, 9521, 31808, 107236, 364364, 1251636, 4333312, 15077986, 52788201, 185909398, 657386742, 2333476922, 8317496562, 29746811372, 106682779598, 383721471229, 1383920063898, 5002364671105, 18120720841491, 65780485710789, 239235254890321, 871545199855827, 3180392395993126

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OFFSET

0,3

LINKS

Table of n, a(n) for n=0..31.

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, 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: A385407 A263375 A148162 * A274775 A039300 A247333

Adjacent sequences: A148160 A148161 A148162 * A148164 A148165 A148166

KEYWORD

nonn,walk

AUTHOR

Manuel Kauers, Nov 18 2008

STATUS

approved