OFFSET
5,1
COMMENTS
Number of 12-subsequences of [ 1, n ] with just 3 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.: 28*(2+x)*x^5/(1-x)^10.
a(n) = C(n+1, 6)*C(n+3, 3). - Zerinvary Lajos, May 13 2005; corrected by R. J. Mathar, Feb 10 2016
From Amiram Eldar, Feb 04 2022: (Start)
Sum_{n>=5} 1/a(n) = 145181/4900 - 3*Pi^2.
Sum_{n>=5} (-1)^(n+1)/a(n) = 3*Pi^2/2 + 2112*log(2)/35 - 277411/4900. (End)
MATHEMATICA
Table[28(n+1) Binomial[n+3, 8]/3, {n, 5, 30}] (* Harvey P. Dale, Oct 24 2020 *)
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Thi Ngoc Dinh (via R. K. Guy)
STATUS
approved