|
|
A174074
|
|
Number of circular permutations of length n without consecutive triples i,i+2,i+4.
|
|
8
|
|
|
1, 1, 1, 2, 6, 22, 109, 657, 4625, 37186, 336336, 3379058, 37328103, 449669577, 5866178493, 82387080624, 1239364493118, 19881771085788, 338797668091565, 6111688544942463, 116354993433563797, 2331395107113471188, 49042688584011866880, 1080639600739277669092, 24891049832682424745839
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
0,4
|
|
COMMENTS
|
Circular permutations are permutations whose indices are from the ring of integers modulo n.
|
|
REFERENCES
|
Wayne M. Dymacek, Isaac Lambert and Kyle Parsons, Arithmetic Progressions in Permutations, http://math.ku.edu/~ilambert/CN.pdf, 2012.
|
|
LINKS
|
|
|
EXAMPLE
|
Since a(5)=22, there are (5-1)!-22=2 circular permutations with consecutive triples i,i+2,i+4 in all circular permutations of length 5. They are exactly (0,2,4,1,3) and (0,2,4,3,1).
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
|
|
EXTENSIONS
|
a(0)-a(2) prepended and terms a(16) onward added by Max Alekseyev, Feb 04 2024
|
|
STATUS
|
approved
|
|
|
|