OFFSET
5,1
COMMENTS
Number of 10-subsequences of [ 1, n ] with just 2 contiguous pairs.
LINKS
Index entries for linear recurrences with constant coefficients, signature (9,-36,84,-126,126,-84,36,-9,1).
FORMULA
G.f.: 7*(3+x)*x^5/(1-x)^9.
a(n) = C(n+1, 6)*C(n+2, 2). - Zerinvary Lajos, Apr 28 2005; corrected by R. J. Mathar, Feb 10 2016
From Amiram Eldar, Feb 04 2022: (Start)
Sum_{n>=5} 1/a(n) = 2969/150 - 2*Pi^2.
Sum_{n>=5} (-1)^(n+1)/a(n) = Pi^2 + 384*log(2)/5 - 3153/50. (End)
MATHEMATICA
Table[7(n+1) Binomial[n+2, 7]/2, {n, 5, 30}] (* Harvey P. Dale, Feb 25 2013 *)
PROG
(PARI) a(n)=7*(n+1)*binomial(n+2, 7)/2 \\ Charles R Greathouse IV, Feb 26 2013
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Thi Ngoc Dinh (via R. K. Guy)
EXTENSIONS
Offset corrected by Harvey P. Dale, Feb 26 2013
STATUS
approved