A150555 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, 0, 0), (0, 0, 1), (1, -1, 0), (1, 0, 1), (1, 1, -1)}.

1, 2, 7, 26, 105, 444, 1933, 8594, 38837, 177733, 821578, 3829041, 17966799, 84784169, 402025974, 1914229705, 9147338010, 43848995372, 210778380404, 1015681669234, 4905000949454, 23734080550789, 115046483612506, 558559093257717, 2715791931567990, 13222091642420811, 64451279207810623

Offset

0,2

Links

Table of n, a(n) for n=0..26.

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, j, -1 + k, -1 + n] + aux[-1 + i, 1 + j, k, -1 + n] + aux[i, j, -1 + k, -1 + n] + aux[1 + i, 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: A150552 A150553 A150554 * A151297 A052706 A150556

Adjacent sequences: A150552 A150553 A150554 * A150556 A150557 A150558

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved