A151213 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), (0, 0, -1), (0, 0, 1), (0, 1, 1), (1, 1, 1)}

1, 3, 13, 55, 251, 1141, 5335, 24963, 118375, 562375, 2691437, 12906257, 62168991, 300007995, 1452102449, 7039558679, 34199832655, 166374726507, 810680032585, 3954666188643, 19315989851281, 94438597716433, 462193556366483, 2263932123478525, 11098618726962151, 54449006317549851, 267313107439106905

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, 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: A264037 A151318 A151212 * A102287 A151214 A151215

Adjacent sequences: A151210 A151211 A151212 * A151214 A151215 A151216

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved