A149752 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, 1), (1, 0, -1), (1, 1, -1), (1, 1, 1)}.

1, 1, 5, 17, 83, 321, 1583, 6671, 33059, 146431, 727601, 3323551, 16541701, 77114047, 384229445, 1816940233, 9060126539, 43292907667, 216000576783, 1040305293295, 5192559536443, 25161578827741, 125631277904691, 611712605108485, 3055029625232447, 14932950312172471, 74593133697689269

Offset

0,3

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, -1 + j, 1 + k, -1 + n] + aux[-1 + i, j, 1 + k, -1 + n] + aux[1 + 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: A303713 A188231 A023253 * A149753 A149754 A149755

Adjacent sequences: A149749 A149750 A149751 * A149753 A149754 A149755

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved