A158733 a(n) = 1225*n^2 + 35.

35, 1260, 4935, 11060, 19635, 30660, 44135, 60060, 78435, 99260, 122535, 148260, 176435, 207060, 240135, 275660, 313635, 354060, 396935, 442260, 490035, 540260, 592935, 648060, 705635, 765660, 828135, 893060, 960435, 1030260, 1102535, 1177260, 1254435, 1334060

Offset

0,1

Comments

The identity (70*n^2 + 1)^2 - (1225*n^2 + 35)*(2*n)^2 = 1 can be written as A158734(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.: -35*(1 + 33*x + 36*x^2)/(x-1)^3.

a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3).

From Amiram Eldar, Mar 22 2023: (Start)

Sum_{n>=0} 1/a(n) = (coth(Pi/sqrt(35))*Pi/sqrt(35) + 1)/70.

Sum_{n>=0} (-1)^n/a(n) = (cosech(Pi/sqrt(35))*Pi/sqrt(35) + 1)/70. (End)

Mathematica

LinearRecurrence[{3, -3, 1}, {35, 1260, 4935}, 50] (* Vincenzo Librandi, Feb 20 2012 *)
1225*Range[0, 30]^2+35 (* Harvey P. Dale, Jul 03 2020 *)

Prog

(Magma) I:=[35, 1260, 4935]; [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 20 2012
(PARI) for(n=0, 40, print1(1225*n^2 + 35", ")); \\ Vincenzo Librandi, Feb 20 2012

Crossrefs

Cf. A005843, A158734.

Sequence in context: A224020 A009979 A238379 * A029560 A195617 A249885

Adjacent sequences: A158730 A158731 A158732 * A158734 A158735 A158736

Keyword

nonn,easy

Author

Vincenzo Librandi, Mar 25 2009

Extensions

Comment rewritten, a(0) added and formula replaced by R. J. Mathar, Oct 22 2009

Status

approved