OFFSET
11,1
COMMENTS
Number of 18-subsequences of [ 1, n ] with just 3 contiguous pairs.
LINKS
T. D. Noe, Table of n, a(n) for n = 11..1000
Index entries for linear recurrences with constant coefficients, signature (16,-120,560,-1820,4368,-8008,11440,-12870,11440,-8008,4368,-1820,560,-120,16,-1).
FORMULA
G.f.: 91*(4+x)*x^11/(1-x)^16.
a(n) = C(n+1, 12)*C(n+3, 3). - Zerinvary Lajos, May 10 2005; corrected by R. J. Mathar, Mar 16 2016
From Amiram Eldar, Feb 02 2022: (Start)
Sum_{n>=11} 1/a(n) = 106810320313/1803601800 - 6*Pi^2.
Sum_{n>=11} (-1)^(n+1)/a(n) = 3*Pi^2 + 5341184*log(2)/5005 - 1387532216767/1803601800. (End)
MATHEMATICA
Table[91 (n + 1) Binomial[n + 3, 14]/3, {n, 11, 33}] (* or *) Table[Binomial[n + 1, 12] Binomial[n + 3, 3], {n, 11, 33}] (* Michael De Vlieger, Mar 16 2016 *)
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Thi Ngoc Dinh (via R. K. Guy)
STATUS
approved