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A149782
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, 1), (-1, 1, 0), (0, -1, 1), (1, 0, -1), (1, 1, 1)}.
0
1, 1, 5, 19, 81, 349, 1553, 7029, 32325, 150063, 703285, 3318075, 15744333, 75062835, 359314751, 1725813897, 8313950559, 40154297311, 194373572835, 942776385651, 4580892115175, 22293571489305, 108649753250187, 530196312054735, 2590311323535195, 12668619137861939, 62019600396603509, 303889836437933503
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[i, 1 + j, -1 + k, -1 + n] + aux[1 + i, -1 + j, k, -1 + n] + aux[1 + i, 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: A317131 A149780 A149781 * A149783 A149784 A240688
KEYWORD
nonn,walk
AUTHOR
Manuel Kauers, Nov 18 2008
STATUS
approved