A150133 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), (-1, 1, -1), (0, 0, 1), (1, 0, -1), (1, 1, 0)}.

1, 2, 6, 20, 72, 267, 1049, 4153, 16997, 70218, 295529, 1253341, 5382995, 23255205, 101325678, 443839080, 1955391369, 8655508361, 38477146051, 171736388543, 769090688549, 3456047601888, 15573006090506, 70374622194835, 318770414771325, 1447381043361075, 6585426723249321, 30023438866364803

Offset

0,2

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, j, 1 + k, -1 + n] + aux[i, j, -1 + k, -1 + n] + aux[1 + i, -1 + 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: A150130 A150131 A150132 * A244783 A216837 A192658

Adjacent sequences: A150130 A150131 A150132 * A150134 A150135 A150136

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved