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A150726 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, -1), (0, 0, 1), (1, 0, -1), (1, 1, 1)}. 0
1, 2, 8, 28, 122, 496, 2256, 9801, 45747, 206259, 976950, 4504593, 21541669, 100830298, 485452210, 2297097380, 11115666088, 53025784640, 257592489664, 1236488167021, 6025167656964, 29064668106315, 141980026810742, 687621457319793, 3365927252920391, 16354699552381265, 80194805724241141 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,2
LINKS
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, j, -1 + k, -1 + n] + aux[1 + i, -1 + 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: A150723 A150724 A150725 * A150727 A150728 A150729
KEYWORD
nonn,walk
AUTHOR
Manuel Kauers, Nov 18 2008
STATUS
approved

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Last modified April 23 20:33 EDT 2024. Contains 371916 sequences. (Running on oeis4.)