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%I #21 Sep 08 2022 08:45:40
%S 1151,4801,10951,19601,30751,44401,60551,79201,100351,124001,150151,
%T 178801,209951,243601,279751,318401,359551,403201,449351,498001,
%U 549151,602801,658951,717601,778751,842401,908551,977201,1048351,1122001
%N a(n) = 1250*n^2 - 100*n + 1.
%C The identity (1250*n^2 - 100*n + 1)^2 - (25*n^2 - 2*n)*(250*n - 10)^2 = 1 can be written as a(n)^2 - A154376(n)*A154378(n)^2 = 1. - _Vincenzo Librandi_, Jan 30 2012
%C This is the case s = 5 of the identity (2*s^4*n^2 - 4*s^2*n + 1)^2 - (s^2*n^2 - 2*n)*(2*s^3*n - 2*s)^2 = 1. - _Bruno Berselli_, Jan 30 2012
%H Vincenzo Librandi, <a href="/A154374/b154374.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) = 3*a(n-1) - 3*a(n-2) + a(n-3). - _Vincenzo Librandi_, Jan 29 2012
%F G.f.: x*(1151 + 1348*x + x^2)/(1-x)^3. - _Vincenzo Librandi_, Jan 29 2012
%F E.g.f.: -1 + (1 + 1150*x + 1250*x^2)*exp(x). - _G. C. Greubel_, Sep 15 2016
%t LinearRecurrence[{3, -3, 1}, {1151, 4801, 10951}, 40] (* _Vincenzo Librandi_, Jan 30 2012 *)
%o (PARI) a(n)=1250*n^2-100*n+1 \\ _Charles R Greathouse IV_, Dec 27 2011
%o (Magma) I:=[1151, 4801, 10951]; [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_, Jan 30 2012
%Y Cf. A154376, A154378.
%K nonn,easy
%O 1,1
%A _Vincenzo Librandi_, Jan 08 2009
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