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A151191
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), (0, 0, 1), (0, 1, 0), (1, 1, -1), (1, 1, 1)}.
0
1, 3, 12, 52, 235, 1089, 5132, 24471, 117690, 569694, 2771599, 13537956, 66339820, 325941961, 1604927091, 7917089993, 39115460328, 193510653777, 958415963991, 4751483624267, 23576263242362, 117069747008544, 581699926248218, 2892041239670253, 14385747925902045, 71590969529821978, 356418752632329264
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, 1 + k, -1 + n] + aux[i, -1 + j, k, -1 + n] + aux[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: A362595 A125187 A151190 * A151192 A151193 A151194
KEYWORD
nonn,walk
AUTHOR
Manuel Kauers, Nov 18 2008
STATUS
approved