# Greetings from The On-Line Encyclopedia of Integer Sequences! http://oeis.org/
Search: id:a093130
Showing 1-1 of 1
%I A093130 #16 Sep 08 2022 08:45:13
%S A093130 0,2,20,160,1200,8800,64000,464000,3360000,24320000,176000000,
%T A093130 1273600000,9216000000,66688000000,482560000000,3491840000000,
%U A093130 25267200000000,182835200000000,1323008000000000,9573376000000000
%N A093130 Third binomial transform of Fibonacci(3n).
%H A093130 G. C. Greubel, Table of n, a(n) for n = 0..1000
%H A093130 Index entries for linear recurrences with constant coefficients, signature (10,-20).
%F A093130 G.f.: 2*x/(1-10*x+20*x^2).
%F A093130 a(n) = ((5+sqrt(5))^n - (5-sqrt(5))^n)/sqrt(5).
%F A093130 a(n) = 2^n*A093131(n).
%F A093130 a(0)=0, a(1)=2, a(n) = 10*a(n-1) - 20*a(n-2). - _Harvey P. Dale_, Jun 24 2015
%F A093130 a(2*n) = 2^(2*n)*5^n*Fibonacci(2*n), a(2*n+1) = 2^(2*n+1)*5^n*Lucas(2*n+1). - _G. C. Greubel_, Dec 27 2019
%p A093130 seq(coeff(series(2*x/(1-10*x+20*x^2), x, n+1), x, n), n = 0..20); # _G. C. Greubel_, Dec 27 2019
%t A093130 LinearRecurrence[{10,-20},{0,2},20] (* _Harvey P. Dale_, Jun 24 2015 *)
%t A093130 Table[If[EvenQ[n], 2^n*5^(n/2)*Fibonacci[n], 2^n*5^((n-1)/2)*LucasL[n]], {n, 0, 20}] (* _G. C. Greubel_, Dec 27 2019 *)
%o A093130 (PARI) my(x='x+O('x^20)); concat([0], Vec(2*x/(1-10*x+20*x^2))) \\ _G. C. Greubel_, Dec 27 2019
%o A093130 (Magma) I:=[0,2]; [n le 2 select I[n] else 10*Self(n-1) - 20*Self(n-2): n in [1..30]]; // _G. C. Greubel_, Dec 27 2019
%o A093130 (Sage)
%o A093130 def A093130_list(prec):
%o A093130 P. = PowerSeriesRing(ZZ, prec)
%o A093130 return P( 2*x/(1-10*x+20*x^2) ).list()
%o A093130 A093130_list(20) # _G. C. Greubel_, Dec 27 2019
%o A093130 (GAP) a:=[0,2];; for n in [3..20] do a[n]:=10*a[n-1]-20*a[n-2]; od; a; # _G. C. Greubel_, Dec 27 2019
%Y A093130 Cf. A000032, A000045.
%K A093130 easy,nonn
%O A093130 0,2
%A A093130 _Paul Barry_, Mar 23 2004
# Content is available under The OEIS End-User License Agreement: http://oeis.org/LICENSE