A136017 a(n) = 36n^2 - 1.

35, 143, 323, 575, 899, 1295, 1763, 2303, 2915, 3599, 4355, 5183, 6083, 7055, 8099, 9215, 10403, 11663, 12995, 14399, 15875, 17423, 19043, 20735, 22499, 24335, 26243, 28223, 30275, 32399, 34595, 36863, 39203, 41615, 44099, 46655, 49283, 51983

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

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

Sequence in context: A327901 A346910 A290560 * A048628 A048629 A133534

Adjacent sequences: A136014 A136015 A136016 * A136018 A136019 A136020

Keyword

nonn,easy

Author

Artur Jasinski, Dec 10 2007

Status

approved