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A150863 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, 0), (1, -1, 1), (1, 0, 0), (1, 1, -1), (1, 1, 1)} 0
1, 2, 8, 32, 144, 654, 3080, 14562, 69904, 336652, 1634408, 7955794, 38912004, 190718078, 937615768, 4617046948, 22782114168, 112556710018, 556894922832, 2758047110028, 13673633536472, 67842394306004, 336866668035624, 1673710798540326, 8320763993997484, 41386470912345362, 205947845365884480 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

Table of n, a(n) for n=0..26.

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[-1 + i, j, k, -1 + n] + aux[-1 + i, 1 + j, -1 + k, -1 + n] + aux[1 + i, 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: A072243 A150861 A150862 * A084137 A129400 A003304

Adjacent sequences:  A150860 A150861 A150862 * A150864 A150865 A150866

KEYWORD

nonn,walk

AUTHOR

Manuel Kauers, Nov 18 2008

STATUS

approved

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Last modified October 14 18:28 EDT 2019. Contains 328022 sequences. (Running on oeis4.)