A148468 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, 1), (0, 0, 1), (1, -1, 0), (1, 1, -1)}.

1, 1, 2, 6, 19, 63, 228, 853, 3303, 13129, 53284, 219809, 920251, 3898392, 16683106, 72047117, 313513987, 1373636939, 6054897529, 26832276225, 119480099586, 534329193514, 2398901718584, 10808275537214, 48854155081710, 221476765120080, 1006775733279628, 4587970914295101, 20956052719317802

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, k, -1 + n] + aux[i, j, -1 + k, -1 + n] + aux[1 + i, 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: A063030 A206463 A148467 * A148469 A191639 A329802

Adjacent sequences: A148465 A148466 A148467 * A148469 A148470 A148471

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved