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
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).
Programs
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Magma
[36*n^2 - 1: n in [1..50]]; // Vincenzo Librandi, Jul 09 2012
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Mathematica
Table[36n^2 - 1, {n, 1, 100}] -
PARI
a(n)=36*n^2-1 \\ Jaume Oliver Lafont, Oct 20 2009
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
Comments