OFFSET
8,1
COMMENTS
Number of 15-subsequences of [ 1, n ] with just 3 contiguous pairs.
LINKS
T. D. Noe, Table of n, a(n) for n = 8..1000
Index entries for linear recurrences with constant coefficients, signature (13,-78,286,-715,1287,-1716,1716,-1287,715,-286,78,-13,1).
FORMULA
G.f.: 55*(3+x)*x^8/(1-x)^13.
a(n) = C(n+1, 9)*C(n+3, 3). - Zerinvary Lajos, May 13 2005; corrected by R. J. Mathar, Mar 16 2016
From Amiram Eldar, Feb 01 2022: (Start)
Sum_{n>=8} 1/a(n) = 9*Pi^2/2 - 5222219/117600.
Sum_{n>=8} (-1)^n/a(n) = 9*Pi^2/4 + 9216*log(2)/35 - 8024887/39200. (End)
MATHEMATICA
Table[55 (n + 1) Binomial[n + 3, 11]/3, {n, 8, 31}] (* or *) Table[Binomial[n + 1, 9] Binomial[n + 3, 3], {n, 8, 31}] (* Michael De Vlieger, Mar 16 2016 *)
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Thi Ngoc Dinh (via R. K. Guy)
STATUS
approved