A148690 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, 0, 1), (1, 0, -1), (1, 1, -1)}.

1, 1, 3, 7, 23, 66, 225, 760, 2635, 9326, 34170, 125303, 465172, 1760793, 6717459, 25686249, 99508522, 388671862, 1520793455, 5988924457, 23774733713, 94606934110, 377603437450, 1516510098070, 6110962006800, 24665305422044, 99964889907241, 406640072920187, 1656607435261793, 6765556140331184

Offset

0,3

Links

Table of n, a(n) for n=0..29.

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, 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: A278455 A060089 A148689 * A148691 A148692 A201204

Adjacent sequences: A148687 A148688 A148689 * A148691 A148692 A148693

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved