A148436 - OEIS

A148436

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

1, 1, 2, 5, 19, 66, 278, 1083, 4749, 19813, 89902, 392386, 1818172, 8165084, 38348338, 175674079, 833439373, 3874392957, 18520418884, 87049560421, 418534476354, 1984090152690, 9583703885386, 45741627148451, 221770286308344, 1064286865852512, 5175830260943097, 24950890970938567, 121651831984621449

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OFFSET

0,3

LINKS

Table of n, a(n) for n=0..28.

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[i, -1 + j, k, -1 + n] + aux[1 + i, -1 + 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: A062122 A148435 A047022 * A148437 A106873 A014273

Adjacent sequences: A148433 A148434 A148435 * A148437 A148438 A148439

KEYWORD

nonn,walk

AUTHOR

Manuel Kauers, Nov 18 2008

STATUS

approved