A149715 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, 0), (0, 1, -1), (1, -1, 1), (1, 1, 1)}.

1, 1, 5, 17, 71, 297, 1299, 5699, 25707, 116793, 536131, 2480397, 11559489, 54122031, 254694451, 1203531177, 5706949229, 27145042957, 129487009863, 619188068719, 2967426010429, 14250219049149, 68558210262343, 330381620037843, 1594552192024995, 7706792146786665, 37296631154429987, 180711774104487389

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[i, -1 + j, 1 + k, -1 + n] + aux[1 + i, 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: A017957 A149713 A149714 * A149716 A324800 A146577

Adjacent sequences: A149712 A149713 A149714 * A149716 A149717 A149718

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved