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A150143 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, 1), (0, 0, 1), (0, 1, -1), (0, 1, 0), (1, -1, 0)} 0
1, 2, 6, 20, 73, 282, 1138, 4740, 20238, 88143, 390061, 1749068, 7929891, 36288683, 167390945, 777445430, 3632416696, 17060267774, 80495119152, 381346095317, 1813181750079, 8649079106026, 41377306954577, 198469912424497, 954244174488097, 4597930637100167, 22198334919108379, 107364372879141877 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

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, k, -1 + n] + aux[i, -1 + j, k, -1 + n] + aux[i, -1 + j, 1 + k, -1 + n] + aux[i, j, -1 + k, -1 + n] + aux[1 + i, 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: A194956 A150141 A150142 * A150144 A243255 A150145

Adjacent sequences:  A150140 A150141 A150142 * A150144 A150145 A150146

KEYWORD

nonn,walk

AUTHOR

Manuel Kauers, Nov 18 2008

STATUS

approved

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Last modified May 25 09:45 EDT 2022. Contains 354066 sequences. (Running on oeis4.)