A149855 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, 1, 0), (0, 0, 1), (1, 0, 0)}.

1, 2, 5, 13, 37, 119, 397, 1364, 4690, 16567, 60099, 221639, 824168, 3076794, 11626300, 44410611, 171024300, 661133266, 2566409626, 10027307231, 39409100079, 155553063846, 615628813008, 2444688640372, 9747085883927, 39001498700419, 156466842555659, 629063961684359, 2535651643941736

Offset

0,2

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, j, k, -1 + n] + aux[i, j, -1 + k, -1 + n] + aux[1 + i, -1 + 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: A148301 A339039 A205544 * A149856 A320175 A064384

Adjacent sequences: A149852 A149853 A149854 * A149856 A149857 A149858

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved