A149742 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, -1, 1), (1, 1, -1), (1, 1, 1)}.

1, 1, 5, 17, 77, 317, 1415, 6333, 28813, 132839, 617129, 2888359, 13611893, 64397119, 306277069, 1461111375, 6994321849, 33574979779, 161548792499, 779091251847, 3764306063501, 18220098464389, 88329628435305, 428817322760587, 2084563208540983, 10145404537779319, 49431229586400457, 241086367397001421

Offset

0,3

Links

Table of n, a(n) for n=0..27.

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, 1 + 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: A149739 A149740 A149741 * A149743 A323794 A151479

Adjacent sequences: A149739 A149740 A149741 * A149743 A149744 A149745

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved