A150808 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, 0, -1), (1, 0, 0), (1, 1, 1)}.

1, 2, 8, 31, 134, 583, 2626, 11941, 55132, 256481, 1203070, 5674137, 26901905, 128059923, 611818639, 2931864809, 14087637504, 67849385837, 327461830936, 1583359892051, 7668728662330, 37197983449726, 180679270560953, 878693067849146, 4278195033300418, 20851542708111455, 101726680363161302

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, -1 + k, -1 + n] + aux[-1 + i, j, k, -1 + n] + aux[i, 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: A150805 A150806 A150807 * A150809 A150810 A150811

Adjacent sequences: A150805 A150806 A150807 * A150809 A150810 A150811

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved