A150425 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, 1), (0, 0, -1), (1, 0, 0), (1, 0, 1)}.

1, 2, 7, 24, 96, 395, 1692, 7319, 32328, 144775, 656618, 3000338, 13806890, 63935867, 297825840, 1393862673, 6549176577, 30879353499, 146076178016, 693066334340, 3296813436279, 15718449300230, 75100784861874, 359528940397209, 1724271608982013, 8283000187595051, 39849493869707366, 191985084989792161

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, j, -1 + k, -1 + n] + aux[-1 + i, j, k, -1 + n] + aux[i, j, 1 + k, -1 + n] + aux[1 + i, -1 + 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: A007162 A150423 A150424 * A102286 A150426 A150427

Adjacent sequences: A150422 A150423 A150424 * A150426 A150427 A150428

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved