|
| |
|
|
A148014
|
|
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, 1, 0), (0, 0, -1), (1, 0, 0)}
|
|
0
|
|
|
|
1, 1, 2, 3, 8, 17, 46, 110, 307, 848, 2420, 6962, 20273, 61162, 185870, 568890, 1757412, 5477941, 17377747, 55272016, 176736009, 568644124, 1842453512, 6025347906, 19741386691, 64938905399, 214606827546, 712767674928, 2380612859574, 7963607476122, 26723258224939, 89989967039606, 304134328175480
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
|
OFFSET
|
0,3
|
|
|
LINKS
|
Table of n, a(n) for n=0..32.
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, j, k, -1 + n] + aux[i, j, 1 + k, -1 + n] + aux[1 + i, -1 + 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: A182889 A219788 A099965 * A148015 A148016 A148017
Adjacent sequences: A148011 A148012 A148013 * A148015 A148016 A148017
|
|
|
KEYWORD
|
nonn,walk
|
|
|
AUTHOR
|
Manuel Kauers, Nov 18 2008
|
|
|
STATUS
|
approved
|
| |
|
|
