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A149171 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, 0, 0), (0, -1, 0), (0, 0, -1), (1, 1, 0)}. 0
1, 1, 4, 10, 33, 115, 391, 1439, 5405, 20303, 79050, 311520, 1230961, 4964657, 20189652, 82314358, 340130593, 1413947795, 5890309480, 24773921096, 104674234969, 443030309859, 1888676636461, 8080601115239, 34621402879031, 149177215251621, 644645021479230, 2789004825787100, 12121746816861675 (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[i, j, 1 + k, -1 + n] + aux[i, 1 + j, k, -1 + n] + aux[1 + i, j, 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: A122948 A317800 A357799 * A149172 A338296 A105680
KEYWORD
nonn,walk
AUTHOR
Manuel Kauers, Nov 18 2008
STATUS
approved

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Last modified April 18 20:18 EDT 2024. Contains 371781 sequences. (Running on oeis4.)