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A148550
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, -1), (-1, 0, 1), (-1, 1, 1), (1, 0, 0)}.
0
1, 1, 3, 5, 21, 44, 189, 433, 1947, 4754, 21843, 55593, 258846, 678794, 3197214, 8581819, 40729683, 111318770, 531516095, 1474157217, 7074437422, 19861550204, 95678831934, 271365160703, 1311627336770, 3752647088859, 18188168212984, 52430062200878, 254708413161552, 739061852992557, 3597755538480279
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, j, k, -1 + n] + aux[1 + i, -1 + j, -1 + k, -1 + n] + aux[1 + i, j, -1 + k, -1 + n] + aux[1 + i, j, 1 + 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: A001775 A148548 A148549 * A148551 A148552 A148553
KEYWORD
nonn,walk
AUTHOR
Manuel Kauers, Nov 18 2008
STATUS
approved