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A150205
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), (0, 0, 1), (0, 1, -1), (0, 1, 0), (1, -1, 1)}.
0
1, 2, 6, 21, 80, 324, 1364, 5907, 26126, 117468, 535060, 2462882, 11434792, 53472391, 251569423, 1189665940, 5650911476, 26945313271, 128916708188, 618616685416, 2976279419487, 14352949350208, 69361426306864, 335825207506769, 1628727206720897, 7911427577875520, 38483370138767232, 187434976370439340
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[i, -1 + j, k, -1 + n] + aux[i, -1 + j, 1 + k, -1 + n] + aux[i, j, -1 + 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: A150204 A129442 A121988 * A150206 A150207 A150208
KEYWORD
nonn,walk
AUTHOR
Manuel Kauers, Nov 18 2008
STATUS
approved