A149529 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, -1, -1), (1, 1, 1)}

1, 1, 5, 11, 55, 167, 799, 2809, 13253, 50221, 237145, 935853, 4453741, 18013565, 86440349, 356002275, 1718466879, 7185616567, 34812951807, 147461259851, 716217783119, 3066285777047, 14926165272107, 64455736815975, 314445779009951, 1367574352109959, 6685030856081887, 29253193559386847

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[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: A018545 A028349 A149528 * A149530 A149531 A083860

Adjacent sequences: A149526 A149527 A149528 * A149530 A149531 A149532

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved