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A149820
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, 1, -1), (0, 1, 0), (1, 0, 0)}.
0
1, 2, 4, 10, 28, 80, 247, 793, 2558, 8550, 29174, 99856, 348717, 1233071, 4370391, 15686057, 56763062, 205799392, 752476359, 2767134060, 10192178158, 37765951585, 140525915462, 523621511694, 1959695454184, 7357711578218, 27658399144870, 104318355674896, 394433880972610, 1492987311881850
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, -1 + 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: A099216 A149819 A276051 * A149821 A149822 A094388
KEYWORD
nonn,walk
AUTHOR
Manuel Kauers, Nov 18 2008
STATUS
approved