OFFSET
4,1
COMMENTS
Number of 11-subsequences of [ 1, n ] with just 3 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*(5+3x)*x^4/(1-x)^9.
a(n) = C(n+1, 5)*C(n+3, 3). - Zerinvary Lajos, May 10 2005; corrected by R. J. Mathar, Feb 10 2016
From Amiram Eldar, Feb 04 2022: (Start)
Sum_{n>=4} 1/a(n) = 5*Pi^2/2 - 2957/120.
Sum_{n>=4} (-1)^n/a(n) = 5*Pi^2/4 + 32*log(2) - 4139/120. (End)
MATHEMATICA
Table[7(n+1)Binomial[n+3, 7], {n, 4, 30}] (* or *) LinearRecurrence[{9, -36, 84, -126, 126, -84, 36, -9, 1}, {35, 336, 1764, 6720, 20790, 55440, 132132, 288288, 585585}, 30] (* Harvey P. Dale, Jan 04 2015 *)
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Thi Ngoc Dinh (via R. K. Guy)
STATUS
approved