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A158630 a(n) = 44*n^2+1. 2
1, 45, 177, 397, 705, 1101, 1585, 2157, 2817, 3565, 4401, 5325, 6337, 7437, 8625, 9901, 11265, 12717, 14257, 15885, 17601, 19405, 21297, 23277, 25345, 27501, 29745, 32077, 34497, 37005, 39601, 42285, 45057, 47917, 50865, 53901, 57025, 60237 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

The identity (44*n^2 + 1)^2 - (484*n^2 + 22)*(2*n)^2 = 1 can be written as a(n)^2 - A158629(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.: -(1 + 42*x + 45*x^2)/(x-1)^3.

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

MATHEMATICA

LinearRecurrence[{3, -3, 1}, {1, 45, 177}, 50] (* Vincenzo Librandi, Feb 17 2012 *)

PROG

(MAGMA) I:=[1, 45, 177]; [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(44*n^2+1", ")); \\ Vincenzo Librandi, Feb 17 2012

CROSSREFS

Cf. A005843, A158629.

Sequence in context: A254147 A271737 A280887 * A158634 A091197 A184539

Adjacent sequences:  A158627 A158628 A158629 * A158631 A158632 A158633

KEYWORD

nonn,easy

AUTHOR

Vincenzo Librandi, Mar 23 2009

EXTENSIONS

Comment rewritten, formula replaced by R. J. Mathar, Oct 28 2009

STATUS

approved

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