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

0,1

Comments

The identity (48*n^2 + 1)^2 - (576*n^2 + 24)*(2*n)^2 = 1 can be written as A158638(n)^2 - a(n)*A005843(n)^2 = 1.

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).

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)

Mathematica

24(24Range[0, 40]^2+1) (* or *) LinearRecurrence[{3, -3, 1}, {24, 600, 2328}, 40] (* Harvey P. Dale, May 23 2011 *)

Prog

(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
(PARI) for(n=0, 40, print1(576*n^2 + 24", ")); \\ Vincenzo Librandi, Feb 17 2012

Crossrefs

Cf. A005843, A158638.

Sequence in context: A009968 A041265 A042106 * A179059 A334281 A055359

Adjacent sequences: A158634 A158635 A158636 * A158638 A158639 A158640

Keyword

nonn,easy

Author

Vincenzo Librandi, Mar 23 2009

Extensions

Comment rephrased and redundant formula replaced by R. J. Mathar, Oct 19 2009

Status

approved