OFFSET
4,1
COMMENTS
Number of 17-subsequences of [ 1, n ] with just 6 contiguous pairs.
LINKS
T. D. Noe, Table of n, a(n) for n = 4..1000
Index entries for linear recurrences with constant coefficients, signature (12,-66,220,-495,792,-924,792,-495,220,-66,12,-1).
FORMULA
G.f.: 42*(5+6*x)*x^4/(1-x)^12.
a(n) = C(n+1,5)*C(n+6,6). - Zerinvary Lajos, Jun 08 2005
From Amiram Eldar, Feb 04 2022: (Start)
Sum_{n>=4} 1/a(n) = 5*Pi^2 - 10444891/211680.
Sum_{n>=4} (-1)^n/a(n) = 5*Pi^2/2 - 512*log(2)/21 - 1644749/211680. (End)
MATHEMATICA
Table[42*(n + 1)*Binomial[n + 6, 10], {n, 4, 30}] (* Amiram Eldar, Feb 04 2022*)
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Thi Ngoc Dinh (via R. K. Guy)
STATUS
approved