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A149351 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), (0, -1, 1), (1, -1, 0), (1, 1, -1), (1, 1, 0)}. 0
1, 1, 4, 12, 42, 156, 606, 2394, 9804, 40802, 172286, 738337, 3202001, 14007442, 61830248, 275035783, 1231198753, 5544051454, 25101208259, 114181560904, 521629518564, 2392582352822, 11013730776909, 50866209238898, 235645872490463, 1094762614098767, 5099330548197097, 23810432651755219 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,3
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, k, -1 + n] + aux[-1 + i, -1 + j, 1 + k, -1 + n] + aux[-1 + i, 1 + j, k, -1 + n] + aux[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: A149348 A149349 A149350 * A149352 A149353 A149354
KEYWORD
nonn,walk
AUTHOR
Manuel Kauers, Nov 18 2008
STATUS
approved

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Last modified April 23 09:48 EDT 2024. Contains 371905 sequences. (Running on oeis4.)