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A149585 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), (-1, 0, 1), (0, 0, -1), (1, 1, 1)} 0
1, 1, 5, 15, 55, 203, 791, 3041, 12057, 48249, 194705, 790373, 3237213, 13323957, 55078721, 228709819, 953594747, 3988265595, 16730145283, 70382381531, 296830291631, 1254604475451, 5314036803363, 22552374316543, 95878895567139, 408287637231539, 1741343710323743, 7437497858831271 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

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, -1 + j, -1 + k, -1 + n] + aux[i, j, 1 + k, -1 + n] + aux[1 + i, j, -1 + 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: A123011 A006358 A054108 * A114947 A316104 A149586

Adjacent sequences:  A149582 A149583 A149584 * A149586 A149587 A149588

KEYWORD

nonn,walk

AUTHOR

Manuel Kauers, Nov 18 2008

STATUS

approved

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Last modified December 13 18:19 EST 2018. Contains 318086 sequences. (Running on oeis4.)