A150807 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, 1), (0, 1, -1), (1, 0, 1), (1, 1, 0)}.

1, 2, 8, 31, 133, 586, 2650, 12189, 56736, 266741, 1262802, 6014765, 28782488, 138282827, 666545461, 3221898963, 15611199126, 75798945036, 368705744764, 1796352068703, 8764345076617, 42815139898679, 209396441863843, 1025148827454705, 5023528239350538, 24637644686786875, 120927928674405187

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, k, -1 + n] + aux[-1 + i, j, -1 + k, -1 + n] + aux[i, -1 + j, 1 + k, -1 + n] + aux[1 + i, 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: A150804 A150805 A150806 * A150808 A150809 A150810

Adjacent sequences: A150804 A150805 A150806 * A150808 A150809 A150810

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved