OFFSET
1,1
COMMENTS
Number of 12-subsequences of [ 1, n ] with just 5 contiguous pairs.
LINKS
Harvey P. Dale, Table of n, a(n) for n = 1..1000
Index entries for linear recurrences with constant coefficients, signature (8,-28,56,-70,56,-28,8,-1).
FORMULA
G.f.: 3*(2+5x)*x/(1-x)^8.
a(n) = C(n+1, 2)*C(n+5, 5). - Zerinvary Lajos, May 26 2005; corrected by R. J. Mathar, Feb 10 2016
From Amiram Eldar, Feb 03 2022: (Start)
Sum_{n>=1} 1/a(n) = 5989/360 - 5*Pi^2/3.
Sum_{n>=1} (-1)^(n+1)/a(n) = 5*Pi^2/6 - 128*log(2)/3 + 7741/360. (End)
MATHEMATICA
Table[3(n+1)Binomial[n+5, 6], {n, 30}] (* or *) LinearRecurrence[{8, -28, 56, -70, 56, -28, 8, -1}, {6, 63, 336, 1260, 3780, 9702, 22176, 46332}, 30] (* or *) CoefficientList[Series[(3(2+5x))/(x-1)^8, {x, 0, 30}], x] (* Harvey P. Dale, Nov 28 2021 *)
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Thi Ngoc Dinh (via R. K. Guy)
STATUS
approved