A148447 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), (-1, 0, 1), (0, 1, 1), (1, 0, -1)}.

1, 1, 2, 6, 17, 50, 171, 567, 1986, 7141, 25843, 96251, 361442, 1374276, 5293874, 20516616, 80360955, 316699197, 1256415912, 5016548166, 20123158508, 81163144236, 328709365541, 1336843859193, 5457904253914, 22356889879962, 91891356641343, 378782930930332, 1565838304801996, 6489933891530336

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[i, -1 + j, -1 + k, -1 + n] + aux[1 + i, 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: A098703 A025272 A356783 * A148448 A148449 A148450

Adjacent sequences: A148444 A148445 A148446 * A148448 A148449 A148450

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved