A150611 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), (0, 1, 1), (1, 0, -1), (1, 0, 1)}.

1, 2, 7, 27, 112, 474, 2099, 9312, 42416, 193697, 896633, 4168473, 19524230, 91810499, 433923397, 2056990221, 9788790658, 46692213723, 223375427972, 1070769264058, 5144335914053, 24758110703837, 119365379127534, 576347361402424, 2786957499742675, 13493556461158656, 65413017891485220

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, j, -1 + k, -1 + n] + aux[-1 + i, j, 1 + k, -1 + n] + aux[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: A150608 A150609 A150610 * A150612 A150613 A150614

Adjacent sequences: A150608 A150609 A150610 * A150612 A150613 A150614

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved