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A148040 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, 0), (0, 1, -1), (1, 0, -1), (1, 0, 0)} 0
1, 1, 2, 3, 8, 19, 55, 152, 475, 1462, 4746, 15587, 53395, 183704, 645336, 2304003, 8369954, 30628353, 113457813, 425476602, 1610303851, 6134996528, 23581388253, 91405898719, 356438621366, 1397836274856, 5518769111515, 21915664391127, 87424025172871, 350422697792128, 1411783576129019, 5711966700811943 (list; graph; refs; listen; history; text; internal format)
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[-1 + i, j, 1 + k, -1 + n] + aux[i, -1 + j, 1 + k, -1 + n] + aux[1 + i, -1 + j, 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: A148038 A326301 A148039 * A148041 A148042 A077269

Adjacent sequences:  A148037 A148038 A148039 * A148041 A148042 A148043

KEYWORD

nonn,walk

AUTHOR

Manuel Kauers, Nov 18 2008

STATUS

approved

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Last modified August 14 04:13 EDT 2020. Contains 336477 sequences. (Running on oeis4.)