A150110 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), (0, 1, -1), (1, 0, 0)}.

1, 2, 6, 19, 69, 266, 1064, 4363, 18277, 77918, 336500, 1468192, 6462863, 28663461, 127926470, 574016728, 2587773401, 11714398489, 53221797551, 242580513410, 1108851682027, 5081788567173, 23344048991986, 107462882959534, 495658287399097, 2290218838590966, 10599364955357158, 49128757432939238

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, k, -1 + n] + aux[i, -1 + j, 1 + 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: A148472 A150108 A150109 * A150111 A150112 A150113

Adjacent sequences: A150107 A150108 A150109 * A150111 A150112 A150113

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved