OFFSET
7,1
COMMENTS
Number of 16-subsequences of [ 1, n ] with just 4 contiguous pairs.
LINKS
T. D. Noe, Table of n, a(n) for n = 7..1000
Index entries for linear recurrences with constant coefficients, signature (13,-78,286,-715,1287,-1716,1716,-1287,715,-286,78,-13,1).
FORMULA
G.f.: 165*(2+x)*x^7/(1-x)^13.
a(n) = C(n+1, 8)*C(n+4, 4). - Zerinvary Lajos, May 26 2005; corrected by R. J. Mathar, Mar 16 2016
From Amiram Eldar, Feb 03 2022: (Start)
Sum_{n>=7} 1/a(n) = 10446643/198450 - 16*Pi^2/3.
Sum_{n>=7} (-1)^(n+1)/a(n) = 8*Pi^2/3 + 8192*log(2)/63 - 23108957/198450. (End)
MATHEMATICA
Table[165 (n + 1) Binomial[n + 4, 11]/4, {n, 7, 30}] (* or *) Table[Binomial[n + 1, 8] Binomial[n + 4, 4], {n, 7, 30}] (* Michael De Vlieger, Mar 16 2016 *)
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Thi Ngoc Dinh (via R. K. Guy)
STATUS
approved