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A148366 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, 0, 1), (-1, 1, 1), (0, 1, 0), (1, -1, 0), (1, 0, -1)} 0
1, 1, 2, 5, 15, 49, 178, 663, 2599, 10464, 43281, 182870, 786326, 3432964, 15178764, 67856987, 306252851, 1393718374, 6389136297, 29478905335, 136795502578, 638051453583, 2989741310540, 14067166927596, 66435732371659, 314823825304590, 1496481124834255, 7133380580616379, 34090715666725451 (list; graph; refs; listen; history; text; internal format)
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, j, 1 + k, -1 + n] + aux[-1 + i, 1 + j, k, -1 + n] + aux[i, -1 + j, k, -1 + n] + aux[1 + i, -1 + j, -1 + k, -1 + n] + aux[1 + i, 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: A149943 A079146 A000734 * A005751 A202182 A149944

Adjacent sequences:  A148363 A148364 A148365 * A148367 A148368 A148369

KEYWORD

nonn,walk

AUTHOR

Manuel Kauers, Nov 18 2008

STATUS

approved

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Last modified March 30 16:16 EDT 2020. Contains 333127 sequences. (Running on oeis4.)