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A149997
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, 0), (-1, 0, -1), (0, 1, 1), (1, -1, -1), (1, 0, 0)}.
0
1, 2, 5, 17, 59, 214, 823, 3214, 12749, 51824, 213137, 886409, 3730703, 15807766, 67446457, 289940695, 1253403583, 5447204342, 23787645787, 104271410457, 458794416353, 2026181571486, 8977296628629, 39895424941238, 177774668991073, 794060282751084, 3555147578359925, 15953110208570535
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, j, k, -1 + n] + aux[-1 + i, 1 + j, 1 + k, -1 + n] + aux[i, -1 + j, -1 + k, -1 + n] + aux[1 + i, j, 1 + k, -1 + n] + aux[1 + i, 1 + 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: A149994 A149995 A149996 * A149998 A149999 A148414
KEYWORD
nonn,walk
AUTHOR
Manuel Kauers, Nov 18 2008
STATUS
approved