OFFSET
3,1
COMMENTS
Number of 10-subsequences of [ 1, n ] with just 3 contiguous pairs.
LINKS
Harvey P. Dale, Table of n, a(n) for n = 3..1000
Index entries for linear recurrences with constant coefficients, signature (8,-28,56,-70,56,-28,8,-1).
FORMULA
G.f.: 5*(4+3x)*x^3/(1-x)^8.
a(n) = C(n+1, 4)*C(n+3, 3) - Zerinvary Lajos, May 10 2005; corrected by R. J. Mathar, Mar 16 2016
From Amiram Eldar, Feb 01 2022: (Start)
Sum_{n>=3} 1/a(n) = 5939/300 - 2*Pi^2.
Sum_{n>=3} (-1)^(n+1)/a(n) = Pi^2 + 64*log(2)/5 - 5609/300. (End)
MATHEMATICA
Table[5(n+1)Binomial[n+3, 6], {n, 3, 30}] (* or *) LinearRecurrence[{8, -28, 56, -70, 56, -28, 8, -1}, {20, 175, 840, 2940, 8400, 20790, 46200, 94380}, 30] (* Harvey P. Dale, Nov 24 2015 *)
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Thi Ngoc Dinh (via R. K. Guy)
STATUS
approved