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%I A084329 #17 Jan 01 2024 11:18:09
%S A084329 0,1,20,380,7200,136400,2584000,48952000,927360000,17568160000,
%T A084329 332816000000,6304956800000,119442816000000,2262757184000000,
%U A084329 42866287360000000,812070603520000000,15384086323200000000
%N A084329 a(0)=0, a(1)=1, a(n)=20a(n-1)-20a(n-2).
%H A084329 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (20,-20).
%F A084329 a(n)=(1/8)*sum(k=0, n, binomial(n, k)*F(6*k)) where F(k) denotes the k-th Fibonacci number.
%F A084329 G.f.: x/(1-20x+20x^2).
%t A084329 Union[Flatten[NestList[{#[[2]],20(#[[2]]-#[[1]])}&,{0,1},20]]]  (* _Harvey P. Dale_, Feb 24 2011 *)
%t A084329 LinearRecurrence[{20,-20},{0,1},20] (* _Harvey P. Dale_, Nov 29 2019 *)
%o A084329 (PARI) a(n)=(1/8)*sum(k=0,n,binomial(n,k)*fibonacci(6*k))
%o A084329 (PARI) a(n)=imag((6+8*quadgen(5))^n)/8
%Y A084329 Cf. A030191.
%K A084329 nonn
%O A084329 0,3
%A A084329 _Benoit Cloitre_, Jun 21 2003

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