%I #50 Sep 26 2024 02:56:18

%S 35,143,323,575,899,1295,1763,2303,2915,3599,4355,5183,6083,7055,8099,

%T 9215,10403,11663,12995,14399,15875,17423,19043,20735,22499,24335,

%U 26243,28223,30275,32399,34595,36863,39203,41615,44099,46655,49283,51983

%N a(n) = 36n^2 - 1.

%C The least common multiple of 6*n+1 and 6*n-1. - _Colin Barker_, Feb 11 2017

%H Vincenzo Librandi, <a href="/A136017/b136017.txt">Table of n, a(n) for n = 1..1000</a>

%H X. Gourdon and P. Sebah, <a href="http://numbers.computation.free.fr/Constants/Pi/piSeries.html">Collection of series for Pi</a>

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/PellEquation.html">Pell Equation</a>

%H Edward Everett Withford, <a href="http://name.umdl.umich.edu/abv2773.0001.001">Pell Equation</a>

%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (3,-3,1).

%F 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

%F a(n) = A061037(12n+10)=(6n-1)*(6n+1). - _Paul Curtz_, Sep 25 2008

%F Sum_{k>=1} (-1)^(k+1)/a(k) = (Pi-3)/6. - _Jaume Oliver Lafont_, Oct 20 2009

%F E.g.f.: 1 + (36 x^2 + 26 x - 1) exp(x). - _Robert Israel_, Jun 09 2016

%F Product_{n >= 1} A016910(n) / a(n) = Pi / 3. - _Fred Daniel Kline_, Jun 09 2016

%F Sum_{n>=1} 1/a(n) = 1/2 - sqrt(3)*Pi/12. - _Amiram Eldar_, Jun 27 2020

%t Table[36n^2 - 1, {n, 1, 100}]

%o (PARI) a(n)=36*n^2-1 \\ _Jaume Oliver Lafont_, Oct 20 2009

%o (Magma)[36*n^2 - 1: n in [1..50]]; // _Vincenzo Librandi_, Jul 09 2012

%Y Cf. A088878, A023208, A136016, A061037, A016910.

%K nonn,easy

%O 1,1

%A _Artur Jasinski_, Dec 10 2007