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A084135 a(n) = 10*a(n-1) - 15*a(n-2), a(0)=1, a(1)=5.

%I A084135 #14 Oct 14 2022 08:55:32
%S A084135 1,5,35,275,2225,18125,147875,1206875,9850625,80403125,656271875,
%T A084135 5356671875,43722640625,356876328125,2912923671875,23776091796875,
%U A084135 194067062890625,1584029251953125,12929286576171875,105532426982421875
%N A084135 a(n) = 10*a(n-1) - 15*a(n-2), a(0)=1, a(1)=5.
%C A084135 Binomial transform of A084134.
%H A084135 G. C. Greubel, <a href="/A084135/b084135.txt">Table of n, a(n) for n = 0..1000</a>
%H A084135 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (10,-15).
%F A084135 a(n) = (5+sqrt(10))^n/2 + (5-sqrt(10))^n/2.
%F A084135 G.f.: (1-5*x)/(1 - 10*x + 15*x^2).
%F A084135 E.g.f.: exp(5*x)*cosh(sqrt(10)*x).
%t A084135 LinearRecurrence[{10,-15},{1,5},30] (* _Harvey P. Dale_, Oct 10 2012 *)
%o A084135 (PARI) a(n)=if(n<0,0,polsym(x^2-10*x+15,n)[1+n]/2)
%o A084135 (Magma) [n le 2 select 5^(n-1) else 10*Self(n-1) -15*Self(n-2): n in [1..30]]; // _G. C. Greubel_, Oct 13 2022
%o A084135 (SageMath)
%o A084135 A084135=BinaryRecurrenceSequence(10,-15,1,5)
%o A084135 [A084135(n) for n in range(41)] # _G. C. Greubel_, Oct 13 2022
%Y A084135 Cf. A084134.
%K A084135 easy,nonn
%O A084135 0,2
%A A084135 _Paul Barry_, May 16 2003