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A148373
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), (-1, 1, -1), (-1, 1, 1), (0, 1, 1), (1, -1, 0)}.
0
1, 1, 2, 5, 16, 42, 147, 456, 1632, 5436, 20292, 70488, 269689, 969337, 3773909, 13915965, 54938959, 206707162, 824983630, 3154624846, 12707736425, 49236197889, 199856276902, 783059335216, 3199277833991, 12653886671347, 51990768945312, 207320788847683, 855980959792228, 3437646542249170
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, 1 + j, k, -1 + n] + aux[i, -1 + j, -1 + k, -1 + n] + aux[1 + i, -1 + j, -1 + k, -1 + n] + aux[1 + 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: A148370 A148371 A148372 * A132734 A148374 A182884
KEYWORD
nonn,walk
AUTHOR
Manuel Kauers, Nov 18 2008
STATUS
approved