A150770 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, 0, 0), (0, 0, -1), (1, 0, 0), (1, 1, 1)}.

1, 2, 8, 30, 128, 551, 2450, 11032, 50478, 232937, 1085177, 5086575, 23984271, 113611413, 540413923, 2579476276, 12350731189, 59294369466, 285353149406, 1376172818179, 6649649064765, 32186279252284, 156035943399738, 757519998218711, 3682389598680916, 17921784874501360, 87319248714390897

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, -1 + j, -1 + k, -1 + n] + aux[-1 + i, j, k, -1 + n] + aux[i, j, 1 + k, -1 + n] + aux[1 + i, 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: A150767 A150768 A150769 * A150771 A150772 A150773

Adjacent sequences: A150767 A150768 A150769 * A150771 A150772 A150773

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved