A148057 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, -1, 1), (-1, 1, 0), (0, 1, -1), (1, 0, 0)}.

1, 1, 2, 3, 10, 22, 65, 166, 562, 1648, 5199, 16864, 57266, 191065, 643174, 2276667, 8015333, 28228639, 101105139, 370143123, 1348702341, 4928075168, 18351289405, 68700034715, 256666572281, 966636795221, 3682287354587, 14030329659617, 53521499184005, 206034637093149, 796949050223031, 3081474368398721

Offset

0,3

Links

Table of n, a(n) for n=0..31.

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, 1 + k, -1 + n] + aux[1 + i, -1 + j, k, -1 + n] + aux[1 + i, 1 + 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: A079078 A285794 A148056 * A148058 A148059 A089880

Adjacent sequences: A148054 A148055 A148056 * A148058 A148059 A148060

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved