A148781 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, 0, 0), (0, 1, -1), (1, -1, -1), (1, 0, 1)}.

1, 1, 3, 8, 23, 81, 280, 977, 3604, 13639, 52495, 204309, 809815, 3254081, 13151968, 53676309, 221332075, 919068872, 3840205474, 16141523490, 68250278556, 290038761654, 1237578756865, 5303354547855, 22822808433377, 98575512487716, 427174939588696, 1857042440689138, 8097662637790062

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, j, -1 + k, -1 + n] + aux[-1 + i, 1 + j, 1 + k, -1 + n] + aux[i, -1 + j, 1 + k, -1 + n] + aux[1 + i, 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: A047143 A148779 A148780 * A327151 A317362 A309114

Adjacent sequences: A148778 A148779 A148780 * A148782 A148783 A148784

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved