A150788 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), (1, 0, 1), (1, 1, -1), (1, 1, 0)}

1, 2, 8, 30, 136, 580, 2753, 12444, 60241, 280841, 1374083, 6526155, 32135134, 154489239, 763821842, 3703025640, 18358658426, 89543838530, 444787699907, 2179253032373, 10839929560975, 53294309035054, 265366430999969, 1308194109799558, 6518921651047642, 32205801829801516, 160582826643012618

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, -1 + j, 1 + k, -1 + n] + aux[-1 + 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: A036723 A150786 A150787 * A150789 A150790 A150791

Adjacent sequences: A150785 A150786 A150787 * A150789 A150790 A150791

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved