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A158636 a(n) = 576*n^2 - 24. 1
552, 2280, 5160, 9192, 14376, 20712, 28200, 36840, 46632, 57576, 69672, 82920, 97320, 112872, 129576, 147432, 166440, 186600, 207912, 230376, 253992, 278760, 304680, 331752, 359976, 389352, 419880, 451560, 484392, 518376, 553512, 589800 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

The identity (48*n^2 - 1)^2 - (576*n^2 - 24)*(2*n)^2 = 1 can be written as A065532(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

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

FORMULA

G.f.: 24*x*(-23 - 26*x + x^2)/(x-1)^3.

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

MATHEMATICA

LinearRecurrence[{3, -3, 1}, {552, 2280, 5160}, 50] (* Vincenzo Librandi, Feb 17 2012 *)

PROG

(Magma) I:=[552, 2280, 5160]; [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(576*n^2 - 24", ")); \\ Vincenzo Librandi, Feb 17 2012

CROSSREFS

Cf. A005843, A065532.

Sequence in context: A203629 A119897 A014360 * A251161 A189549 A282595

Adjacent sequences: A158633 A158634 A158635 * A158637 A158638 A158639

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 November 26 20:01 EST 2022. Contains 358362 sequences. (Running on oeis4.)