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A158543 a(n) = 144*n^2 - 12. 2

%I

%S 132,564,1284,2292,3588,5172,7044,9204,11652,14388,17412,20724,24324,

%T 28212,32388,36852,41604,46644,51972,57588,63492,69684,76164,82932,

%U 89988,97332,104964,112884,121092,129588,138372,147444,156804,166452

%N a(n) = 144*n^2 - 12.

%C The identity (24*n^2 - 1)^2 - (144*n^2 - 12)*(2*n)^2 = 1 can be written as A158544(n)^2 - a(n)*A005843(n)^2 = 1.

%H Vincenzo Librandi, <a href="/A158543/b158543.txt">Table of n, a(n) for n = 1..10000</a>

%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (3,-3,1).

%F G.f.: -x*(132 + 168*x - 12*x^2)/(x-1)^3. - _Vincenzo Librandi_, Feb 14 2012

%F a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3). - _Vincenzo Librandi_, Feb 14 2012

%t LinearRecurrence[{3, -3, 1}, {132, 564, 1284}, 50] (* _Vincenzo Librandi_, Feb 14 2012 *)

%t 144*Range[40]^2-12 (* _Harvey P. Dale_, Oct 20 2012 *)

%o (MAGMA) I:=[132, 564, 1284]; [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 14 2012

%o (PARI) for(n=1, 40, print1(144*n^2 - 12", ")); \\ _Vincenzo Librandi_, Feb 14 2012

%Y Cf. A005843, A158544.

%K nonn,easy

%O 1,1

%A _Vincenzo Librandi_, Mar 21 2009

%E Comment rewritten by _R. J. Mathar_, Oct 16 2009

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Last modified September 20 08:13 EDT 2019. Contains 327214 sequences. (Running on oeis4.)