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A149708 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), (1, -1, 1), (1, 0, -1), (1, 1, 1)}. 0
1, 1, 5, 17, 71, 275, 1197, 5015, 22283, 96237, 432479, 1908495, 8659109, 38763863, 177016943, 800411443, 3674033371, 16740426241, 77162216045, 353660756327, 1635698336915, 7532360479213, 34938080545161, 161509862609757, 750995241429291, 3482801514066409, 16229200948512393, 75468695084619587 (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, -1 + k, -1 + n] + aux[-1 + i, j, 1 + k, -1 + n] + aux[-1 + i, 1 + j, -1 + 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: A273852 A146511 A128887 * A149709 A149710 A149711
KEYWORD
nonn,walk
AUTHOR
Manuel Kauers, Nov 18 2008
STATUS
approved

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Last modified April 28 02:01 EDT 2024. Contains 372020 sequences. (Running on oeis4.)