A148683 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), (0, 0, -1), (1, 0, -1), (1, 1, 0)}.

1, 1, 3, 7, 22, 66, 227, 758, 2741, 9861, 36917, 138933, 535499, 2077759, 8190950, 32516955, 130479483, 527198671, 2147012696, 8795672388, 36264715700, 150285288597, 626008650470, 2619473550761, 11007963517106, 46439591494941, 196648771804289, 835525524895916, 3561426453988150

Offset

0,3

Links

Table of n, a(n) for n=0..28.

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, k, -1 + n] + aux[-1 + i, j, 1 + k, -1 + n] + aux[i, j, 1 + 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: A007595 A148681 A148682 * A148684 A148685 A365452

Adjacent sequences: A148680 A148681 A148682 * A148684 A148685 A148686

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved