A150412 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, 1, -1), (0, 1, -1), (1, 0, 1), (1, 1, 0)}.

1, 2, 7, 24, 95, 373, 1553, 6488, 27816, 120095, 525451, 2314243, 10274611, 45865522, 205856259, 927951641, 4199784173, 19073273163, 86892341253, 396957455389, 1818035505139, 8345474366040, 38388848038163, 176923857185482, 816825507464054, 3777234390492518, 17493175265642425, 81127205888809701

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, k, -1 + n] + aux[-1 + i, j, -1 + k, -1 + n] + aux[i, -1 + j, 1 + k, -1 + n] + aux[1 + 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: A150409 A150410 A150411 * A150413 A150414 A150415

Adjacent sequences: A150409 A150410 A150411 * A150413 A150414 A150415

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved