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A150586
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, 0), (0, -1, 1), (0, 1, 1), (1, 0, 0), (1, 1, -1)}.
0
1, 2, 7, 26, 110, 479, 2172, 10002, 46834, 221461, 1056587, 5074301, 24505397, 118882368, 578908059, 2828055381, 13852580674, 68010146230, 334558354721, 1648583112673, 8135656937555, 40200921378838, 198871293465675, 984787005486642, 4880863318364261, 24209845939798547, 120168684450652892
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, j, k, -1 + n] + aux[i, -1 + j, -1 + k, -1 + n] + aux[i, 1 + j, -1 + k, -1 + n] + aux[1 + i, 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: A150583 A150584 A150585 * A196709 A150587 A001862
KEYWORD
nonn,walk
AUTHOR
Manuel Kauers, Nov 18 2008
STATUS
approved