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%I #13 Sep 08 2022 08:45:12
%S 1,5,30,200,1400,10000,72000,520000,3760000,27200000,196800000,
%T 1424000000,10304000000,74560000000,539520000000,3904000000000,
%U 28249600000000,204416000000000,1479168000000000,10703360000000000
%N a(n) = 10*a(n-1) - 20*a(n-2), a(0)=1,a(1)=5.
%C Fifth binomial transform of (1, 0, 5, 0, 25, 0, ...).
%H G. C. Greubel, <a href="/A090139/b090139.txt">Table of n, a(n) for n = 0..1000</a>
%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (10,-20).
%F a(n) = ((5-sqrt(5))^n + (5+sqrt(5))^n)/2.
%F a(n) = Sum_{k=0..floor(n/2)} C(n, 2k) * 5^(n-k).
%F a(n) = Sum_{k=0..n} C(n, k) * 5^(n-k/2) * (1+(-1)^k)/2.
%F a(n) = Sum_{k=0..n} 5^k*A098158(n,k). - _Philippe Deléham_, Dec 04 2006
%F G.f.: (1-5*x)/(1-10*x+20*x^2). - _G. C. Greubel_, Aug 02 2019
%t LinearRecurrence[{10, -20}, {1,5}, 30] (* _G. C. Greubel_, Aug 02 2019 *)
%o (PARI) my(x='x+O('x^30)); Vec((1-5*x)/(1-10*x+20*x^2)) \\ _G. C. Greubel_, Aug 02 2019
%o (Magma) I:=[1,5]; [n le 2 select I[n] else 10*Self(n-1) -20*Self(n-2): n in [1..30]]; // _G. C. Greubel_, Aug 02 2019
%o (Sage) ((1-5*x)/(1-10*x+20*x^2)).series(x, 30).coefficients(x, sparse=False) # _G. C. Greubel_, Aug 02 2019
%o (GAP) a:=[1,5];; for n in [3..30] do a[n]:=10*a[n-1]-20*a[n-2]; od; a; # _G. C. Greubel_, Aug 02 2019
%K easy,nonn
%O 0,2
%A _Paul Barry_, Nov 22 2003
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