A150192 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, 1, -1), (0, 0, 1), (1, 0, -1), (1, 1, 0)}.

1, 2, 6, 21, 78, 304, 1231, 5135, 21902, 95027, 418304, 1862817, 8376414, 37974948, 173371141, 796374923, 3677865850, 17066625367, 79532418735, 372042497296, 1746330581438, 8222474044021, 38823835970023, 183784136405180, 872043766342655, 4146741853151268, 19757920098144071, 94313939720198119

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[-1 + i, 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, -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: A150190 A356780 A150191 * A287211 A357538 A150193

Adjacent sequences: A150189 A150190 A150191 * A150193 A150194 A150195

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved