A150593 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, 0), (0, 1, -1), (0, 1, 0), (1, 0, -1), (1, 1, 1)}.

1, 2, 7, 27, 105, 434, 1823, 7806, 33899, 148480, 656977, 2924911, 13103957, 58999404, 266766771, 1210995905, 5514878065, 25192059976, 115378537393, 529692971635, 2437090152723, 11234658689688, 51884773874329, 240009946904894, 1111939544334635, 5158739770169646, 23964572305570459, 111461502853365199

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, 1 + k, -1 + n] + aux[i, -1 + j, k, -1 + n] + aux[i, -1 + j, 1 + k, -1 + n] + aux[1 + i, 1 + 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: A129013 A150591 A150592 * A024429 A136412 A360149

Adjacent sequences: A150590 A150591 A150592 * A150594 A150595 A150596

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved