A150158 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, 0), (0, 0, 1), (1, 0, 0), (1, 1, -1)}.

1, 2, 6, 20, 74, 295, 1217, 5190, 22647, 100615, 453645, 2068934, 9529304, 44244248, 206843859, 972671829, 4597078503, 21822430463, 103989554045, 497216087260, 2384517334224, 11466062259600, 55266814345883, 266960111496512, 1292020237869313, 6264036962958085, 30418111852726110, 147925273925223569

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, 1 + k, -1 + n] + aux[-1 + i, j, k, -1 + n] + aux[i, j, -1 + k, -1 + n] + aux[1 + i, -1 + j, 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: A145867 A188144 A245734 * A034010 A135588 A318402

Adjacent sequences: A150155 A150156 A150157 * A150159 A150160 A150161

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved