A151096 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), (0, 0, -1), (0, 0, 1), (0, 1, 0), (1, 0, 1)}.

1, 3, 11, 43, 180, 774, 3420, 15325, 69736, 320177, 1484157, 6921368, 32488328, 153168686, 725511789, 3447958237, 16443901747, 78628116041, 376994548410, 1811341325055, 8721864511612, 42069122806563, 203276074637444, 983628465137718, 4766650411566060, 23127163122865459, 112348695687372996

Offset

0,2

Links

Table of n, a(n) for n=0..26.

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, k, -1 + n] + aux[i, j, -1 + k, -1 + n] + aux[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: A149071 A149072 A284720 * A151097 A151098 A277220

Adjacent sequences: A151093 A151094 A151095 * A151097 A151098 A151099

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved