A150039 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, 1, 0), (0, 1, 1), (1, -1, 0)}.

1, 2, 6, 17, 65, 229, 908, 3446, 14423, 57647, 245981, 1016795, 4424472, 18716285, 82476997, 355146413, 1580936927, 6900405318, 30965367150, 136621486303, 617120493890, 2746863685508, 12475299646207, 55934938905828, 255213981896563, 1151328462568785, 5273980232350123, 23917051605529728

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[i, -1 + j, -1 + k, -1 + n] + aux[i, -1 + j, 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: A150036 A150037 A150038 * A150040 A346043 A079456

Adjacent sequences: A150036 A150037 A150038 * A150040 A150041 A150042

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved