OFFSET
2,1
COMMENTS
Number of 11-subsequences of [ 1, n ] with just 4 contiguous pairs.
LINKS
Index entries for linear recurrences with constant coefficients, signature (8,-28,56,-70,56,-28,8,-1).
FORMULA
G.f.: 5*(3+4x)*x^2/(1-x)^8.
a(n) = C(n+1, 3)*C(n+4, 4) - Zerinvary Lajos, May 10 2005; corrected by R. J. Mathar, Feb 10 2016
From Amiram Eldar, Feb 04 2022: (Start)
Sum_{n>=2} 1/a(n) = 2*Pi^2 - 5899/300.
Sum_{n>=2} (-1)^n/a(n) = Pi^2 - 64*log(2)/5 - 281/300. (End)
MATHEMATICA
Table[5 * (n+1) * Binomial[n+4, 6], {n, 2, 50}] (* Amiram Eldar, Feb 04 2022 *)
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Thi Ngoc Dinh (via R. K. Guy)
STATUS
approved