A158371 - OEIS

A158371

576n^2 - 2n.

574, 2300, 5178, 9208, 14390, 20724, 28210, 36848, 46638, 57580, 69674, 82920, 97318, 112868, 129570, 147424, 166430, 186588, 207898, 230360, 253974, 278740, 304658, 331728, 359950, 389324, 419850, 451528, 484358, 518340, 553474, 589760

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OFFSET

1,1

COMMENTS

The identity (576*n-1)^2-(576*n^2-2*n)*(24)^2=1 can be written as A158372(n)^2-a(n)*(24)^2=1.

LINKS

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

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

E. J. Barbeau, Polynomial Excursions, Chapter 10: Diophantine equations (2010), pages 84-85 (row 15 in the first table at p. 85, case d(t) = t*(24^2*t-2)).

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

FORMULA

Contribution from Harvey P. Dale, Nov 06 2011: (Start)

G.f.: -2*x*(289*x+287)/(x-1)^3.

a(1)=574, a(2)=2300, a(3)=5178, a(n) = 3*a(n-1)-3*a(n-2)+a(n-3). (End)

MATHEMATICA

Table[576n^2-2n, {n, 40}] (* or *) LinearRecurrence[{3, -3, 1}, {574, 2300, 5178}, 40] (* Harvey P. Dale, Nov 06 2011 *)

PROG

(Magma) I:=[574, 2300, 5178]; [n le 3 select I[n] else 3*Self(n-1)-3*Self(n-2)+1*Self(n-3): n in [1..50]];

(PARI) a(n) = 576*n^2 - 2*n.

CROSSREFS

Cf. A158372.