A149779 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), (-1, 0, 1), (0, -1, 0), (1, 1, -1), (1, 1, 1)}.

1, 1, 5, 19, 79, 345, 1519, 6753, 31275, 144213, 670297, 3163775, 14936953, 70792149, 338585227, 1619921411, 7770795003, 37481336509, 180882640119, 874507511059, 4243254642229, 20599950232899, 100141184353091, 488025883714483, 2379533504908105, 11614032821371989, 56787761956069469, 277795759408103433

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, k, -1 + n] + aux[1 + 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: A149777 A149778 A163609 * A125657 A111929 A146030

Adjacent sequences: A149776 A149777 A149778 * A149780 A149781 A149782

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved