OFFSET
1,1
COMMENTS
Fourth row of the 7-rowed array A113807. - Giovanni Teofilatto, Oct 26 2009 [crossref added by Wolfdieter Lang, Dec 15 2011]
LINKS
David Lovler, Table of n, a(n) for n = 1..1000
Index entries for linear recurrences with constant coefficients, signature (1,1,-1).
FORMULA
From R. J. Mathar, Aug 13 2008: (Start)
a(n) = 7n - ((-1)^n + 7)/2.
G.f.: 2x*(2 + 3x + 2x^2)/((1-x)^2*(1+x)). (End)
a(n) = 14*n - a(n-1) - 14 (with a(1)=4). - Vincenzo Librandi, Aug 01 2010
Sum_{n>=1} (-1)^(n+1)/a(n) = tan(3*Pi/14)*Pi/14. - Amiram Eldar, Dec 30 2021
E.g.f.: 4 + ((14*x - 7)*exp(x) - exp(-x))/2. - David Lovler, Sep 04 2022
a(n) = 2*A047385(n). - Michel Marcus, Sep 05 2022
MATHEMATICA
Select[Range[2, 400, 2], MemberQ[{4, 10}, Mod[#, 14]]&] (* or *) LinearRecurrence[{1, 1, -1}, {4, 10, 18}, 60] (* Harvey P. Dale, Jan 08 2023 *)
PROG
(PARI) a(n)=7*n-((-1)^n+7)/2 \\ Charles R Greathouse IV, Dec 27 2011
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Giovanni Teofilatto, Jan 22 2006
EXTENSIONS
More terms from Neven Juric, Apr 10 2008
STATUS
approved