A150983 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, 0), (0, 0, -1), (0, 1, 1), (1, 1, 1)}.

1, 2, 9, 37, 159, 718, 3291, 15204, 71157, 336016, 1594541, 7604721, 36443467, 175245232, 845045739, 4085978081, 19802983411, 96159057034, 467735169447, 2278801528917, 11117744645581, 54307350516844, 265579468667673, 1300114105128236, 6370466002605131, 31241369973015994, 153331939935728111

Offset

0,2

Links

Table of n, a(n) for n=0..26.

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[i, -1 + j, -1 + k, -1 + n] + aux[i, j, 1 + k, -1 + n] + aux[i, 1 + j, 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: A106851 A129169 A162548 * A150984 A150985 A150986

Adjacent sequences: A150980 A150981 A150982 * A150984 A150985 A150986

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved