A150947 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, 0), (0, 0, -1), (1, 0, 1), (1, 1, 1)}.

1, 2, 9, 35, 151, 680, 3091, 14151, 66604, 312709, 1477845, 7064187, 33776392, 161972289, 782054269, 3776621763, 18274150703, 88793910636, 431582703033, 2100537100068, 10251967952026, 50052164785199, 244606975187753, 1197729068318476, 5866583177051961, 28756777564864878, 141158695193821810

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[-1 + i, j, -1 + k, -1 + n] + aux[i, j, 1 + k, -1 + n] + aux[1 + i, -1 + j, 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: A289782 A150945 A150946 * A110224 A363549 A150948

Adjacent sequences: A150944 A150945 A150946 * A150948 A150949 A150950

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved