A149543 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, 0), (-1, 0, 0), (1, 0, -1), (1, 1, 1)}

1, 1, 5, 13, 55, 183, 797, 2857, 12745, 48137, 217181, 848805, 3864969, 15476641, 70950761, 289401315, 1333805235, 5519509311, 25548231703, 106962811299, 496860515253, 2100326275693, 9785578824799, 41701885468869, 194788901960581, 835866986360113, 3912959749894971, 16891828897637735

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, j, 1 + k, -1 + n] + aux[1 + i, j, k, -1 + n] + aux[1 + i, 1 + j, 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: A089794 A216821 A039510 * A149544 A149545 A149546

Adjacent sequences: A149540 A149541 A149542 * A149544 A149545 A149546

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved