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A157476 2048n^2 + 128n + 1. 3
2177, 8449, 18817, 33281, 51841, 74497, 101249, 132097, 167041, 206081, 249217, 296449, 347777, 403201, 462721, 526337, 594049, 665857, 741761, 821761, 905857, 994049, 1086337, 1182721, 1283201, 1387777, 1496449, 1609217, 1726081, 1847041 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

The identity (2048*n^2+128*n+1)^2-(16*n^2+n)*(512*n+16)^2=1 can be written as a(n)^2-A157474(n)*A157475(n)^2=1.

This is the case s=4 of the identity (8*n^2*s^4+8*n*s^2+1)^2 - (n^2*s^2+n)*(8*n*s^3+4*s)^2 = 1. - Bruno Berselli, Jan 25 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

Contribution from Harvey P. Dale, Aug 15 2011. (Start)

G.f.: x*(-x^2-1918*x-2177)/(x-1)^3.

a(1)=2177, a(2)=8449, a(3)=18817, a(n)=3*a(n-1)-3*a(n-2)+a(n-3). (End)

MATHEMATICA

Table[2048n^2+128n+1, {n, 30}] (* or *) LinearRecurrence[{3, -3, 1}, {2177, 8449, 18817}, 30] (* Harvey P. Dale, Aug 15 2011 *)

PROG

(PARI) a(n)=2048*n^2+128*n+1 \\ Charles R Greathouse IV, Jun 17 2017

CROSSREFS

Cf. A157474, A157475.

Sequence in context: A185801 A170776 A250240 * A157853 A072141 A008918

Adjacent sequences:  A157473 A157474 A157475 * A157477 A157478 A157479

KEYWORD

nonn,easy

AUTHOR

Vincenzo Librandi, Mar 01 2009

EXTENSIONS

Comment rewritten by Bruno Berselli, Aug 22 2011

STATUS

approved

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Last modified October 22 17:39 EDT 2019. Contains 328319 sequences. (Running on oeis4.)