A158735 a(n) = 1225*n^2 - 35.

1190, 4865, 10990, 19565, 30590, 44065, 59990, 78365, 99190, 122465, 148190, 176365, 206990, 240065, 275590, 313565, 353990, 396865, 442190, 489965, 540190, 592865, 647990, 705565, 765590, 828065, 892990, 960365, 1030190, 1102465, 1177190, 1254365, 1333990, 1416065

Offset

1,1

Comments

The identity (70*n^2 - 1)^2 - (1225*n^2 - 35)*(2*n)^2 = 1 can be written as A158736(n)^2 - a(n)*A005843(n)^2 = 1.

Links

Vincenzo Librandi, Table of n, a(n) for n = 1..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*x*(-34 - 37*x + 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>=1} 1/a(n) = (1 - cot(Pi/sqrt(35))*Pi/sqrt(35))/70.

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

Mathematica

LinearRecurrence[{3, -3, 1}, {1190, 4865, 10990}, 50] (* Vincenzo Librandi, Feb 20 2012 *)
1225Range[30]^2-35 (* Harvey P. Dale, May 08 2021 *)

Prog

(Magma) I:=[1190, 4865, 10990]; [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=1, 40, print1(1225*n^2 - 35", ")); \\ Vincenzo Librandi, Feb 20 2012

Crossrefs

Cf. A005843, A158736.

Sequence in context: A233687 A233640 A252643 * A035860 A290843 A298239

Adjacent sequences: A158732 A158733 A158734 * A158736 A158737 A158738

Keyword

nonn,easy

Author

Vincenzo Librandi, Mar 25 2009

Extensions

Comment rewritten and formula replaced by R. J. Mathar, Oct 22 2009

Status

approved