OFFSET
1,1
COMMENTS
Numbers m such that m^2 == 2 (mod 7). - Vincenzo Librandi, Aug 05 2010
Numbers k such that A056107(k)/7 is an integer. - Bruno Berselli, Feb 14 2017
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
a(n)^2 = 7*A056834(a(n)) + 2. - Bruno Berselli, Nov 28 2010
G.f.: x*(3 + x + 3*x^2)/((1 + x)*(1 - x)^2). - R. J. Mathar, Oct 08 2011
Sum_{n>=1} (-1)^(n+1)/a(n) = Pi*tan(Pi/14)/7. - Amiram Eldar, Dec 12 2021
E.g.f.: 3 + ((14*x - 7)*exp(x) - 5*exp(-x))/4. - David Lovler, Sep 01 2022
From Amiram Eldar, Nov 22 2024: (Start)
Product_{n>=1} (1 - (-1)^n/a(n)) = 1.
Product_{n>=1} (1 + (-1)^n/a(n)) = 2*cos(Pi/7) - 1 (A160389 - 1). (End)
MATHEMATICA
LinearRecurrence[{1, 1, -1}, {3, 4, 10}, 50] (* Amiram Eldar, Dec 12 2021 *)
PROG
(PARI) a(n) = (14*n-5*(-1)^n-7)/4 \\ Charles R Greathouse IV, Jun 11 2015
CROSSREFS
KEYWORD
nonn,easy,changed
AUTHOR
STATUS
approved