A151048 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, 1, 1), (0, 0, 1), (0, 1, 0), (1, 0, 0)}.

1, 3, 10, 35, 134, 541, 2245, 9423, 40264, 174677, 765999, 3378993, 15015062, 67172893, 302152668, 1363987239, 6181971004, 28123733683, 128357658619, 587218526389, 2693201631582, 12381487370775, 57042683267028, 263242929396829, 1216926606638440, 5634919151844065, 26131475075744005

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, k, -1 + n] + aux[i, -1 + j, k, -1 + n] + aux[i, j, -1 + k, -1 + n] + aux[1 + i, -1 + j, -1 + 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: A084781 A151047 A008984 * A149038 A097148 A149039

Adjacent sequences: A151045 A151046 A151047 * A151049 A151050 A151051

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved