OFFSET
1,1
COMMENTS
Also, numbers n such that (n^2+3)/7 is a nonnegative integer. - Bruno Berselli, Jan 16 2016
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
G.f.: x*(2 + 3*x + 2*x^2) / ( (1+x)*(x-1)^2 ). - R. J. Mathar, Dec 05 2011
a(n) = (14*n - (-1)^n - 7)/4. - Bruno Berselli, Dec 05 2011
a(n) = 4*n - 2 - floor(n/2). - Wesley Ivan Hurt, Oct 16 2013
E.g.f.: 2 + ((14*x - 7)*exp(x) - exp(-x))/4. - David Lovler, Sep 01 2022
From Amiram Eldar, Sep 26 2022: (Start)
a(n) = A113804(n)/2.
Sum_{n>=1} (-1)^(n+1)/a(n) = tan(3*Pi/14)*Pi/7. (End)
From Amiram Eldar, Nov 22 2024: (Start)
Product_{n>=1} (1 - (-1)^n/a(n)) = 2*sin(3*Pi/14) (A255249).
Product_{n>=1} (1 + (-1)^n/a(n)) = 1/(2*cos(Pi/7)) (A255240). (End)
MAPLE
MATHEMATICA
Table[4 n - 2 - Floor[n/2], {n, 100}] (* Wesley Ivan Hurt, Oct 16 2013 *)
#+{2, 5}&/@(7*Range[0, 30])//Flatten (* Harvey P. Dale, Jul 15 2017 *)
PROG
(PARI) a(n)=(14*n-6)>>2 \\ Charles R Greathouse IV, Dec 05 2011
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
STATUS
approved
