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A151106 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, 0), (1, 1, 0)}. 0
1, 3, 11, 44, 188, 834, 3796, 17595, 82652, 392296, 1876988, 9038428, 43750078, 212672939, 1037483310, 5076179561, 24898992612, 122392690133, 602735470493, 2972948379238, 14684093287089, 72615661668126, 359478469000610, 1781231772491187, 8833368751277994, 43837986172512587, 217700030074601239 (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, k, -1 + n] + aux[-1 + i, j, 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: A001207 A319156 A026887 * A302186 A151107 A063018
KEYWORD
nonn,walk,changed
AUTHOR
Manuel Kauers, Nov 18 2008
STATUS
approved

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Last modified April 25 06:49 EDT 2024. Contains 371964 sequences. (Running on oeis4.)