OFFSET
1,1
COMMENTS
The least common multiple of 6*n+1 and 6*n-1. - Colin Barker, Feb 11 2017
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 1..1000
X. Gourdon and P. Sebah, Collection of series for Pi
Eric Weisstein's World of Mathematics, Pell Equation
Edward Everett Withford, Pell Equation
Index entries for linear recurrences with constant coefficients, signature (3,-3,1).
FORMULA
O.g.f.: x*(-35-38*x+x^2)/(-1+x)^3 = 1-35/(-1+x)-108/(-1+x)^2-72/(-1+x)^3. - R. J. Mathar, Dec 12 2007
a(n) = A061037(12n+10)=(6n-1)*(6n+1). - Paul Curtz, Sep 25 2008
Sum_{k>=1} (-1)^(k+1)/a(k) = (Pi-3)/6. - Jaume Oliver Lafont, Oct 20 2009
E.g.f.: 1 + (36 x^2 + 26 x - 1) exp(x). - Robert Israel, Jun 09 2016
Product_{n >= 1} A016910(n) / a(n) = Pi / 3. - Fred Daniel Kline, Jun 09 2016
Sum_{n>=1} 1/a(n) = 1/2 - sqrt(3)*Pi/12. - Amiram Eldar, Jun 27 2020
MATHEMATICA
Table[36n^2 - 1, {n, 1, 100}]
PROG
(PARI) a(n)=36*n^2-1 \\ Jaume Oliver Lafont, Oct 20 2009
(Magma)[36*n^2 - 1: n in [1..50]]; // Vincenzo Librandi, Jul 09 2012
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Artur Jasinski, Dec 10 2007
STATUS
approved