OFFSET
3,1
COMMENTS
Number of 14-subsequences of [ 1, n ] with just 5 contiguous pairs.
LINKS
Index entries for linear recurrences with constant coefficients, signature (10,-45,120,-210,252,-210,120,-45,10,-1).
FORMULA
G.f.: 14*(4+5x)*x^3/(1-x)^10.
a(n) = C(n+1, 4)*C(n+5, 5). - Zerinvary Lajos, May 26 2005; corrected by R. J. Mathar, Feb 10 2016
From Amiram Eldar, Feb 04 2022: (Start)
Sum_{n>=3} 1/a(n) = 290341/8820 - 10*Pi^2/3.
Sum_{n>=3} (-1)^(n+1)/a(n) = 5*Pi^2/3 - 128*log(2)/7 - 3683/980. (End)
MATHEMATICA
Table[14 * (n+1) * Binomial[n+5, 8], {n, 3, 50}] (* Amiram Eldar, Feb 04 2022 *)
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Thi Ngoc Dinh (via R. K. Guy)
STATUS
approved