A157741 a(n) = 388962*n^2 + 1764*n + 1.

390727, 1559377, 3505951, 6230449, 9732871, 14013217, 19071487, 24907681, 31521799, 38913841, 47083807, 56031697, 65757511, 76261249, 87542911, 99602497, 112440007, 126055441, 140448799, 155620081, 171569287, 188296417

Offset

1,1

Comments

The identity (388962*n^2 + 1764*n + 1)^2 - (441*n^2 + 2*n)*(18522*n + 42)^2 = 1 can be written as a(n)^2 - A158321(n)*A157740(n)^2 = 1. - Vincenzo Librandi, Feb 05 2012

This is the case s=21 of the identity (2*n^2*s^4 + 4*n*s^2 + 1)^2 - (n^2*s^2 + 2*n)*(2*n*s^3 + 2*s)^2 = 1. - Vincenzo Librandi, Feb 05 2012

Links

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

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

Formula

G.f.: x*(390727 + 387196*x + x^2)/(1-x)^3. - Vincenzo Librandi, Feb 05 2012

a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3). - Vincenzo Librandi, Feb 05 2012

a(n) = 2*A158322(n)^2 - 1. - Bruno Berselli, Feb 05 2011

Mathematica

LinearRecurrence[{3, -3, 1}, {390727, 1559377, 3505951}, 50] (* Vincenzo Librandi, Feb 05 2012 *)

Prog

(Magma) I:=[390727, 1559377, 3505951]; [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 05 2012
(PARI) for(n=1, 40, print1(388962*n^2 + 1764*n + 1", ")); \\ Vincenzo Librandi, Feb 05 2012

Crossrefs

Cf. A157740, A158321.

Sequence in context: A017336 A017456 A017588 * A345612 A346329 A345622

Adjacent sequences: A157738 A157739 A157740 * A157742 A157743 A157744

Keyword

nonn,easy

Author

Vincenzo Librandi, Mar 05 2009

Status

approved