A149209 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, 0, 1), (1, -1, -1), (1, -1, 1), (1, 1, 0)}.

1, 1, 4, 10, 40, 134, 527, 1950, 7904, 30491, 125199, 498445, 2067864, 8381254, 35053759, 144098563, 606147761, 2516740364, 10640646802, 44529824218, 189010047669, 795948814046, 3390234316109, 14349091499960, 61296338029127, 260536427436212, 1115820095516391, 4759539900355647

Offset

0,3

Links

Table of n, a(n) for n=0..27.

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[-1 + i, 1 + j, -1 + k, -1 + n] + aux[-1 + i, 1 + j, 1 + k, -1 + n] + aux[1 + i, 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: A149207 A156798 A149208 * A053792 A032121 A149210

Adjacent sequences: A149206 A149207 A149208 * A149210 A149211 A149212

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved