OFFSET
5,1
COMMENTS
Number of 8-subsequences of [ 1, n ] with just 1 contiguous pair.
36*a(n) is the number of permutations of (n+1) symbols that 6-commute with an (n+1)-cycle (see A233440 for definition), where 36 = A000757(6). - Luis Manuel Rivera MartÃnez, Feb 07 2014
LINKS
Luis Manuel Rivera, Integer sequences and k-commuting permutations, arXiv preprint arXiv:1406.3081 [math.CO], 2014-2015.
Index entries for linear recurrences with constant coefficients, signature (8,-28,56,-70,56,-28,8,-1).
FORMULA
G.f.: (6+x)*x^5/(1-x)^8.
From Amiram Eldar, Jan 30 2022: (Start)
Sum_{n>=5} 1/a(n) = 3019/300 - Pi^2.
Sum_{n>=5} (-1)^(n+1)/a(n) = Pi^2/2 + 512*log(2)/5 - 22729/300. (End)
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Thi Ngoc Dinh (via R. K. Guy)
STATUS
approved