A149107 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), (0, 0, 1), (0, 1, -1), (1, 0, -1), (1, 1, -1)}.

1, 1, 4, 8, 34, 91, 409, 1253, 5796, 19316, 91012, 321297, 1532547, 5642190, 27148463, 103193047, 499754109, 1947944739, 9480548621, 37710917710, 184252596026, 745269843131, 3652708303943, 14983349164891, 73623316529978, 305628346362958, 1504922749359266, 6311850874007876, 31134553886877543

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, 1 + k, -1 + n] + aux[-1 + i, j, 1 + k, -1 + n] + aux[i, -1 + j, 1 + k, -1 + n] + aux[i, 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: A149104 A149105 A149106 * A197157 A324410 A218628

Adjacent sequences: A149104 A149105 A149106 * A149108 A149109 A149110

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved