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A151056
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, 0, 1), (0, 1, 0), (1, 0, 0)}.
0
1, 3, 10, 37, 146, 602, 2558, 11117, 49164, 220488, 1000026, 4578134, 21122894, 98108364, 458281644, 2151336893, 10142872712, 48003142708, 227953126694, 1085755952438, 5185537890802, 24826512875604, 119123452553134, 572732936690052, 2758696070434436, 13310240295982516, 64318937543766884
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[i, -1 + j, k, -1 + n] + aux[i, 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: A299501 A226434 A151055 * A109081 A366231 A046632
KEYWORD
nonn,walk
AUTHOR
Manuel Kauers, Nov 18 2008
STATUS
approved