OFFSET
2,1
COMMENTS
Number of 7-subsequences of [ 1, n ] with just 2 contiguous pairs.
LINKS
Index entries for linear recurrences with constant coefficients, signature (6,-15,20,-15,6,-1).
FORMULA
G.f.: 2*(3+2x)*x^2/(1-x)^6.
a(n) = 2*A006411(n+1).
a(n) = C(n+1, 3)*C(n+2, 2) - Zerinvary Lajos, May 13 2005, corrected by R. J. Mathar, Feb 13 2016
From Amiram Eldar, Jan 28 2022: (Start)
Sum_{n>=2} 1/a(n) = Pi^2 - 29/3.
Sum_{n>=2} (-1)^n/a(n) = Pi^2/2 + 8*log(2) - 31/3. (End)
MATHEMATICA
Table[2(n+1)Binomial[n+2, 4], {n, 2, 35}] (* Harvey P. Dale, Feb 03 2011 *)
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Thi Ngoc Dinh (via R. K. Guy)
STATUS
approved