A148982 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, 0, 0), (1, -1, 0), (1, -1, 1), (1, 0, 1), (1, 1, -1)}.

1, 1, 3, 9, 32, 112, 421, 1605, 6355, 25406, 103844, 428179, 1791014, 7548478, 32138386, 137694930, 594387179, 2579410260, 11258896341, 49364497947, 217448108770, 961501842191, 4267820443221, 19005590638727, 84908412272243, 380406367033615, 1708968248146308, 7696452279135478, 34743630238766412

Offset

0,3

Links

Table of n, a(n) for n=0..28.

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[-1 + i, 1 + j, -1 + k, -1 + n] + aux[-1 + i, 1 + j, k, -1 + n] + aux[1 + i, 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: A148979 A148980 A148981 * A148983 A148984 A289611

Adjacent sequences: A148979 A148980 A148981 * A148983 A148984 A148985

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved