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A148858 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, 0, 0), (0, -1, 1), (1, 0, 1), (1, 1, -1)} 0
1, 1, 3, 8, 28, 96, 349, 1266, 4872, 18937, 74824, 300666, 1221397, 5003868, 20748125, 86640057, 363955361, 1541316904, 6561178732, 28057372888, 120671313034, 521071872996, 2258015020869, 9827393809110, 42906980263767, 187868103415443, 825367631777135, 3635500398284390, 16050904740944003 (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, -1 + j, 1 + k, -1 + n] + aux[-1 + i, j, -1 + k, -1 + n] + aux[i, 1 + j, -1 + k, -1 + n] + aux[1 + i, 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: A241585 A273162 A148857 * A148859 A148860 A148861

Adjacent sequences:  A148855 A148856 A148857 * A148859 A148860 A148861

KEYWORD

nonn,walk

AUTHOR

Manuel Kauers, Nov 18 2008

STATUS

approved

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Last modified April 20 06:36 EDT 2019. Contains 322294 sequences. (Running on oeis4.)