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%I #31 Sep 08 2022 08:45:13
%S 0,1,4,15,48,145,420,1183,3264,8865,23780,63151,166320,434993,1130948,
%T 2925375,7533312,19323713,49395780,125877071,319888560,810893265,
%U 2050891876,5176349663,13040153280,32793453025,82337215012,206424991215
%N a(n) = n * Pell(n).
%C Binomial transform of A093968.
%H Harry J. Smith, <a href="/A093967/b093967.txt">Table of n, a(n) for n = 0..1000</a>
%H Rigoberto Flórez, Robinson Higuita and Alexander Ramírez, <a href="https://arxiv.org/abs/1808.01264">The resultant, the discriminant, and the derivative of generalized Fibonacci polynomials</a>, arXiv:1808.01264 [math.NT], 2018.
%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (4,-2,-4,-1).
%F G.f.: x*(1+x^2)/(1 - 2*x - x^2)^2;
%F a(n) = n*((1+sqrt(2))^n - (1-sqrt(2))^n)/(2*sqrt(2));
%F a(n) = n * A000129(n).
%p seq(fibonacci(n,2)*n, n=0..27); # _Zerinvary Lajos_, Apr 05 2008
%t LinearRecurrence[{4,-2,-4,-1}, {0,1,4,15}, 30] (* _Vincenzo Librandi_, Dec 20 2015 *)
%o (PARI) { default(realprecision, 100); s=sqrt(2); for (n=0, 100, a=n*round(((1+s)^n-(1-s)^n)/(2*s)); write("b093967.txt", n, " ", a); ) } \\ _Harry J. Smith_, Jun 17 2009
%o (Magma) I:=[0,1,4,15]; [n le 4 select I[n] else 4*Self(n-1)-2*Self(n-2)-4*Self(n-3)-Self(n-4): n in [1..40]]; // _Vincenzo Librandi_, Dec 20 2015
%o (Sage) [n*lucas_number1(n,2,-1) for n in (0..30)] # _G. C. Greubel_, Dec 28 2021
%Y Cf. A000129, A006645, A023607, A093835.
%K easy,nonn
%O 0,3
%A _Paul Barry_, Apr 21 2004
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