A148741 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, 1), (-1, 1, 0), (1, -1, 0), (1, 0, 0), (1, 1, -1)}.

1, 1, 3, 7, 26, 80, 324, 1150, 4908, 18964, 83715, 341998, 1545368, 6563356, 30163671, 131790446, 613435908, 2738122567, 12871074729, 58410682449, 276719975340, 1272372258459, 6065901435994, 28187798326093, 135077703165596, 633152138248192, 3047152900049867, 14385841999184273, 69484774027121302

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, j, k, -1 + n] + aux[-1 + i, 1 + j, k, -1 + n] + aux[1 + i, -1 + j, k, -1 + n] + aux[1 + i, 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: A296852 A208979 A148740 * A328280 A258311 A184459

Adjacent sequences: A148738 A148739 A148740 * A148742 A148743 A148744

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved