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A158733 a(n) = 1225*n^2 + 35. 2
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 (list; graph; refs; listen; history; text; internal format)
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

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).

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

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Last modified May 11 00:21 EDT 2021. Contains 343784 sequences. (Running on oeis4.)