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A151224 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), (0, 0, -1), (0, 1, 1), (1, 0, 1), (1, 1, 1)} 0
1, 3, 13, 57, 269, 1263, 6087, 29353, 143181, 699193, 3434479, 16889777, 83336909, 411613143, 2037184517, 10091009051, 50051745221, 248426942387, 1234175744599, 6134692833341, 30513666460305, 151840379791795, 755948217025833, 3764882415978347, 18757386744070867, 93480023140520929 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

Table of n, a(n) for n=0..25.

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[i, j, 1 + 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: A151319 A151222 A151223 * A151225 A326984 A296771

Adjacent sequences:  A151221 A151222 A151223 * A151225 A151226 A151227

KEYWORD

nonn,walk

AUTHOR

Manuel Kauers, Nov 18 2008

STATUS

approved

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Last modified July 16 11:09 EDT 2020. Contains 335784 sequences. (Running on oeis4.)