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URL: https://oeis.org/A150921

⇱ A150921 - OEIS

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A150921
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, 0), (0, 0, -1), (1, 1, 0), (1, 1, 1)}.
0
1, 2, 9, 33, 145, 620, 2767, 12458, 56879, 261838, 1216407, 5678117, 26682723, 125847796, 596177017, 2833553145, 13508052345, 64572800642, 309401003271, 1485722170179, 7148272797563, 34452552963828, 166322187950381, 804104736390432, 3892832802399421, 18869556315728514, 91571013610329289
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, -1 + k, -1 + n] + aux[-1 + i, -1 + j, k, -1 + n] + aux[i, j, 1 + k, -1 + n] + aux[1 + i, j, 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: A215695 A289600 A202206 * A150922 A150923 A150924
KEYWORD
nonn,walk
AUTHOR
Manuel Kauers, Nov 18 2008
STATUS
approved