A148628 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, 0, 1), (-1, 1, 0), (1, -1, -1), (1, 0, 1)}.

1, 1, 3, 6, 22, 54, 212, 601, 2431, 7403, 30839, 98930, 419323, 1398292, 6000768, 20625494, 89442109, 314563659, 1375653111, 4932398161, 21712296506, 79108779880, 350198380740, 1293249911490, 5752818251686, 21491825170513, 95996936457124, 362276515435840, 1623971067403002, 6183008648651877

Offset

0,3

Links

Table of n, a(n) for n=0..29.

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, 1 + j, 1 + k, -1 + n] + aux[1 + i, -1 + j, k, -1 + n] + aux[1 + i, 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: A148625 A148626 A148627 * A148629 A151264 A148630

Adjacent sequences: A148625 A148626 A148627 * A148629 A148630 A148631

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved