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%I #51 Oct 11 2022 00:36:09
%S -1,5,19,41,71,109,155,209,271,341,419,505,599,701,811,929,1055,1189,
%T 1331,1481,1639,1805,1979,2161,2351,2549,2755,2969,3191,3421,3659,
%U 3905,4159,4421,4691,4969,5255,5549,5851,6161,6479,6805,7139,7481,7831,8189,8555,8929,9311,9701,10099,10505,10919,11341
%N a(n) = 4*n^2 - 6*n + 1.
%H Vincenzo Librandi, <a href="/A125202/b125202.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 a(n) = A125199(n,n-1) for n>1.
%F A003415(a(n)) = A017089(n-1).
%F From _Arkadiusz Wesolowski_, Dec 25 2011: (Start)
%F a(1) = -1, a(n) = a(n-1) + 8*n - 10.
%F a(n) = 2*a(n-1) - a(n-2) + 8 with a(1) = -1 and a(2) = 5.
%F G.f.: (1 - 4*x + 11*x^2)/(1 - x)^3. (End)
%F a(n) = A002943(n-1) - 1. - _Arkadiusz Wesolowski_, Feb 15 2012
%F a(n) = A028387(2n-3), with A028387(-1) = -1. - _Vincenzo Librandi_, Oct 10 2013
%F E.g.f.: exp(x)*(1 - 2*x + 4*x^2). - _Stefano Spezia_, Oct 10 2022
%t f[a_]:=4*a^2-6*a+1; lst={};Do[AppendTo[lst,f[n]],{n,0,5!}];lst (* _Vladimir Joseph Stephan Orlovsky_, Jul 14 2009 *)
%o (Magma) [4*n^2 - 6*n + 1: n in [1..60]]; // _Vincenzo Librandi_, Jul 11 2011
%o (PARI) a(n)=4*n^2-6*n+1 \\ _Charles R Greathouse IV_, Sep 28 2015
%Y Cf. A125199.
%Y Cf. A003415, A017089.
%Y Cf. A002939, A016789, A017041, A017485, A028387.
%Y Cf. A002943, A028387.
%K sign,easy
%O 1,2
%A _Reinhard Zumkeller_, Nov 24 2006
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