A149739 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, 0), (-1, 0, 0), (1, -1, 1), (1, 1, -1), (1, 1, 1)}

1, 1, 5, 17, 77, 307, 1417, 6181, 28841, 130211, 616889, 2855129, 13626469, 63959761, 307535581, 1459756265, 7050834891, 33718778041, 163569203413, 787091296573, 3829522559929, 18511523389995, 90315167541557, 438264679672285, 2142658648810825, 10428805196818487, 51083374056751217, 249282000240638829

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, -1 + j, 1 + k, -1 + n] + aux[-1 + i, 1 + j, -1 + k, -1 + n] + aux[1 + i, j, k, -1 + n] + aux[1 + i, 1 + j, 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: A126956 A149737 A149738 * A149740 A149741 A149742

Adjacent sequences: A149736 A149737 A149738 * A149740 A149741 A149742

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved