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a(n) = 2*A079291(n) (twice squares of Pell numbers).
3

%I #23 Mar 15 2024 23:20:32

%S 0,2,8,50,288,1682,9800,57122,332928,1940450,11309768,65918162,

%T 384199200,2239277042,13051463048,76069501250,443365544448,

%U 2584123765442,15061377048200,87784138523762,511643454094368

%N a(n) = 2*A079291(n) (twice squares of Pell numbers).

%H G. C. Greubel, <a href="/A114619/b114619.txt">Table of n, a(n) for n = 0..1000</a>

%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (5,5,-1).

%F a(n) = 2*A000129(n)^2.

%F G.f.: 2*x*(1-x)/((1+x)*(1-6*x+x^2)).

%F a(n) = A001333(n)^2 - (-1)^n. - Antonio Pane (apane1(AT)spc.edu), Dec 15 2007

%t 2*Fibonacci[Range[0, 30], 2]^2 (* _G. C. Greubel_, Aug 18 2022 *)

%o (Magma) [n le 3 select 2*(n-1)^2 else 5*Self(n-1) +5*Self(n-2) -Self(n-3): n in [1..31]]; // _G. C. Greubel_, Aug 18 2022

%o (SageMath) [2*lucas_number1(n,2,-1)^2 for n in (0..30)] # _G. C. Greubel_, Aug 18 2022

%Y Cf. A000129, A001109, A001333, A001542, A079291.

%Y Cf. also A090390, A108475, A114619, A116484.

%K easy,nonn

%O 0,2

%A _Creighton Dement_, Feb 17 2006

%E Entry revised by _N. J. A. Sloane_, Mar 15 2024