A158010 - OEIS

A158010

a(n) = 256*n^2 - n.

255, 1022, 2301, 4092, 6395, 9210, 12537, 16376, 20727, 25590, 30965, 36852, 43251, 50162, 57585, 65520, 73967, 82926, 92397, 102380, 112875, 123882, 135401, 147432, 159975, 173030, 186597, 200676, 215267, 230370, 245985, 262112, 278751, 295902

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OFFSET

1,1

COMMENTS

The identity (512*n - 1)^2 - (256*n^2 - n)*32^2 = 1 can be written as A158011(n)^2 - a(n)*32^2 = 1. - Vincenzo Librandi, Feb 10 2012

LINKS

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

E. J. Barbeau, Polynomial Excursions, Chapter 10: Diophantine equations (2010), pages 84-85 (row 14 in the first table at p. 85, case d(t) = t*(16^2*t-1)).

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

FORMULA

G.f.: x*(-255 - 257*x)/(x-1)^3. - Vincenzo Librandi, Feb 10 2012

a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3). - Vincenzo Librandi, Feb 10 2012

MATHEMATICA

Table[256n^2-n, {n, 50}] (* Harvey P. Dale, Mar 30 2011 *)

LinearRecurrence[{3, -3, 1}, {255, 1022, 2301}, 50] (* Vincenzo Librandi, Feb 10 2012 *)

PROG

(Magma) I:=[255, 1022, 2301]; [n le 3 select I[n] else 3*Self(n-1)-3*Self(n-2)+1*Self(n-3): n in [1..50]]; // Vincenzo Librandi, Feb 10 2012

(PARI) for(n=1, 50, print1(256*n^2 - n", ")); \\ Vincenzo Librandi, Feb 10 2012

CROSSREFS

Cf. A158011.