A158637 a(n) = 576*n^2 + 24.
24, 600, 2328, 5208, 9240, 14424, 20760, 28248, 36888, 46680, 57624, 69720, 82968, 97368, 112920, 129624, 147480, 166488, 186648, 207960, 230424, 254040, 278808, 304728, 331800, 360024, 389400, 419928, 451608, 484440, 518424, 553560, 589848, 627288, 665880, 705624
Offset: 0
Links
- Vincenzo Librandi, Table of n, a(n) for n = 0..10000
- Vincenzo Librandi, X^2-AY^2=1, Math Forum, 2007. [Wayback Machine link]
- Index entries for linear recurrences with constant coefficients, signature (3,-3,1).
Programs
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Magma
I:=[24, 600, 2328]; [n le 3 select I[n] else 3*Self(n-1)-3*Self(n-2)+1*Self(n-3): n in [1..40]]; // Vincenzo Librandi, Feb 17 2012
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Mathematica
24(24Range[0,40]^2+1) (* or *) LinearRecurrence[{3,-3,1},{24, 600, 2328}, 40] (* Harvey P. Dale, May 23 2011 *) -
PARI
for(n=0, 40, print1(576*n^2 + 24", ")); \\ Vincenzo Librandi, Feb 17 2012
Formula
G.f.: -24*(1 + 22*x + 25*x^2)/(x-1)^3.
a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3).
From Amiram Eldar, Mar 19 2023: (Start)
Sum_{n>=0} 1/a(n) = (coth(Pi/(2*sqrt(6)))*Pi/(2*sqrt(6)) + 1)/48.
Sum_{n>=0} (-1)^n/a(n) = (cosech(Pi/(2*sqrt(6)))*Pi/(2*sqrt(6)) + 1)/48. (End)
From Elmo R. Oliveira, Jan 15 2025: (Start)
E.g.f.: 24*exp(x)*(1 + 24*x + 24*x^2).
a(n) = 24*A158547(n). (End)
Extensions
Comment rephrased and redundant formula replaced by R. J. Mathar, Oct 19 2009
Comments