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A157912 64*n^2 + 16. 2
80, 272, 592, 1040, 1616, 2320, 3152, 4112, 5200, 6416, 7760, 9232, 10832, 12560, 14416, 16400, 18512, 20752, 23120, 25616, 28240, 30992, 33872, 36880, 40016, 43280, 46672, 50192, 53840, 57616, 61520, 65552, 69712, 74000, 78416, 82960 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

The identity (8*n^2+1)^2-(64*n^2+16)*n^2 = 1 can be written as A081585(n)^2-a(n)*n^2 = 1. - Vincenzo Librandi, Feb 09 2012

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

G.f.: x*(80+32*x+16*x^2)/(1-x)^3. - Vincenzo Librandi, Feb 09 2012

a(n) = 3*a(n-1)-3*a(n-2)+a(n-3). - Vincenzo Librandi, Feb 09 2012

MAPLE

A157912:=n->64*n^2 + 16: seq(A157912(n), n=1..50); # Wesley Ivan Hurt, Oct 27 2014

MATHEMATICA

64Range[50]^2+16 (* Harvey P. Dale, Mar 24 2011 *)

LinearRecurrence[{3, -3, 1}, {80, 272, 592}, 40] (* Vincenzo Librandi, Feb 09 2012 *)

PROG

(Magma) I:=[80, 272, 592]; [n le 3 select I[n] else 3*Self(n-1)-3*Self(n-2)+Self(n-3): n in [1..50]]; // Vincenzo Librandi, Feb 09 2012

(PARI) for(n=1, 40, print1(64*n^2 + 16", ")); \\ Vincenzo Librandi, Feb 09 2012

CROSSREFS

Cf. A081585.

Sequence in context: A235091 A306434 A234890 * A234883 A194646 A057441

Adjacent sequences: A157909 A157910 A157911 * A157913 A157914 A157915

KEYWORD

nonn,easy

AUTHOR

Vincenzo Librandi, Mar 09 2009

STATUS

approved

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Last modified December 3 09:50 EST 2022. Contains 358517 sequences. (Running on oeis4.)