A150646 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), (-1, 0, 0), (0, 1, 1), (1, 0, 1), (1, 1, -1)}.

1, 2, 7, 28, 115, 500, 2222, 10067, 46210, 214561, 1005078, 4737301, 22463677, 107029474, 511992191, 2457370516, 11830812439, 57106820758, 276269824537, 1339241424340, 6503928190006, 31636482948413, 154107605564757, 751681548781630, 3670810368631306, 17945609466718551, 87818303399821312

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, -1 + k, -1 + n] + aux[i, -1 + j, -1 + k, -1 + n] + aux[1 + i, j, 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: A289158 A012855 A224066 * A364145 A128611 A061539

Adjacent sequences: A150643 A150644 A150645 * A150647 A150648 A150649

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved