A148981 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, 0, 1), (0, 1, 1), (1, -1, 1), (1, 1, -1)}.

1, 1, 3, 9, 32, 112, 419, 1556, 5966, 22800, 88624, 343953, 1348203, 5280871, 20811229, 81995438, 324318955, 1282789042, 5086938010, 20174850237, 80153717254, 318501840735, 1267153768678, 5042296615421, 20081851469220, 79994363147594, 318851212604716, 1271134164676675, 5069865013260048

Offset

0,3

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, -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, -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: A148978 A148979 A148980 * A148982 A148983 A148984

Adjacent sequences: A148978 A148979 A148980 * A148982 A148983 A148984

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved