A149711 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, 1), (1, 0, -1), (1, 1, 1)}.

1, 1, 5, 17, 71, 281, 1231, 5153, 22979, 99543, 448661, 1983701, 9013777, 40398115, 184691161, 835861357, 3839728657, 17505347027, 80728468785, 370148336231, 1712533995729, 7888147455237, 36596079171987, 169199785485739, 786850584292555, 3649384577801451, 17006530772430431, 79086079258651029

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, j, 1 + k, -1 + 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]]; Table[Sum[aux[i, j, k, n], {i, 0, n}, {j, 0, n}, {k, 0, n}], {n, 0, 10}]

Crossrefs

Sequence in context: A149708 A149709 A149710 * A149712 A017957 A149713

Adjacent sequences: A149708 A149709 A149710 * A149712 A149713 A149714

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved