A150038 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), (0, 1, 1), (1, 0, -1)}.

1, 2, 6, 17, 64, 227, 871, 3359, 13652, 55101, 227586, 952299, 4035236, 17138824, 73679165, 319022507, 1387532405, 6062569327, 26665424994, 117732051064, 521367618463, 2318281418998, 10347358968360, 46293263460427, 207664385024191, 934331922022978, 4213432619406459, 19037141901560433

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, j, 1 + k, -1 + n] + aux[i, -1 + 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: A000661 A150036 A150037 * A150039 A150040 A346043

Adjacent sequences: A150035 A150036 A150037 * A150039 A150040 A150041

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved