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A158634 a(n) = 46*n^2 - 1. 2
45, 183, 413, 735, 1149, 1655, 2253, 2943, 3725, 4599, 5565, 6623, 7773, 9015, 10349, 11775, 13293, 14903, 16605, 18399, 20285, 22263, 24333, 26495, 28749, 31095, 33533, 36063, 38685, 41399, 44205, 47103, 50093, 53175, 56349, 59615, 62973 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

The identity (46*n^2 - 1)^2 - (529*n^2 - 23)*(2*n)^2 = 1 can be written as a(n)^2 - A158633(n)*A005843(n)^2 = 1.

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 1..10000

Vincenzo Librandi, X^2-AY^2=1

Index entries for linear recurrences with constant coefficients, signature (3,-3,1).

FORMULA

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

G.f.: x*(-45 - 48*x + x^2)/(x-1)^3.

MATHEMATICA

LinearRecurrence[{3, -3, 1}, {45, 183, 413}, 50] (* Vincenzo Librandi, Feb 17 2012 *)

PROG

(MAGMA) I:=[45, 183, 413]; [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=1, 40, print1(46*n^2 - 1", ")); \\ Vincenzo Librandi, Feb 17 2012

CROSSREFS

Cf. A005843, A158633.

Sequence in context: A271737 A280887 A158630 * A091197 A184539 A146302

Adjacent sequences:  A158631 A158632 A158633 * A158635 A158636 A158637

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

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Last modified September 23 22:32 EDT 2020. Contains 337315 sequences. (Running on oeis4.)