OFFSET
0,2
COMMENTS
Previous name was: Sequence gives X values that satisfy the integer equation 2*X^3 + 3*X^2 = Y^2.
To find Y values: b(n) = (2*n^2 + 2*n - 1)*(2*n - 1).
LINKS
G. C. Greubel, Table of n, a(n) for n = 0..5000
Index entries for linear recurrences with constant coefficients, signature (3, -3, 1).
FORMULA
a(n) = 2*n^2 + 2*n - 1 for n>=1.
G.f.: x*(1+x)*(3-x)/(1-x)^3. - R. J. Mathar, Nov 14 2007
E.g.f.: 1 + (2*x^2 + 4*x -1)*exp(x). - G. C. Greubel, Jul 13 2017
From Amiram Eldar, Mar 07 2021: (Start)
Sum_{n>=1} 1/a(n) = 1 + sqrt(3)*Pi*tan(sqrt(3)*Pi/2)/6.
Product_{n>=1} (1 + 1/a(n)) = -Pi*sec(sqrt(3)*Pi/2)/2.
Product_{n>=1} (1 - 1/a(n)) = cos(sqrt(5)*Pi/2)*sec(sqrt(3)*Pi/2)/2. (End)
MATHEMATICA
Join[{0}, LinearRecurrence[{3, -3, 1}, {3, 11, 23}, 40]] (* Vincenzo Librandi, Sep 22 2015 *)
PROG
(Magma) [0] cat [2*n^2+2*n-1: n in [1..50]]; // Vincenzo Librandi, Sep 22 2015
(PARI) for(n=0, 50, print1(if(n==0, 0, 2*n^2 + 2*n -1), ", ")) \\ G. C. Greubel, Jul 13 2017
CROSSREFS
KEYWORD
nonn
AUTHOR
Mohamed Bouhamida, Nov 06 2007
EXTENSIONS
Edited by the Associate Editors of the OEIS, Nov 15 2009
More terms from Vincenzo Librandi, Sep 22 2015
Shorter name (using formula given) from Joerg Arndt, Sep 27 2015
STATUS
approved