A148467 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, 0), (0, 0, 1), (1, -1, 1), (1, 1, -1)}.

1, 1, 2, 6, 19, 63, 228, 849, 3279, 12970, 52391, 215143, 896069, 3776720, 16080646, 69082912, 299088374, 1303775401, 5718074120, 25214654439, 111731999692, 497294169489, 2222212374035, 9966362357271, 44846949907442, 202420181884867, 916209119602653, 4157777698180396, 18913437500393274

Offset

0,3

Links

Table of n, a(n) for n=0..28.

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, 1 + j, -1 + k, -1 + n] + aux[i, j, -1 + k, -1 + n] + aux[1 + i, j, 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: A063030 A372531 A206463 * A148468 A148469 A191639

Adjacent sequences: A148464 A148465 A148466 * A148468 A148469 A148470

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved