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A180250 a(n) = 5*a(n-1) + 10*a(n-2), with a(1)=0 and a(2)=1.

%I A180250 #24 Jul 21 2023 04:21:41
%S A180250 0,1,5,35,225,1475,9625,62875,410625,2681875,17515625,114396875,
%T A180250 747140625,4879671875,31869765625,208145546875,1359425390625,
%U A180250 8878582421875,57987166015625,378721654296875,2473479931640625,16154616201171875,105507880322265625
%N A180250 a(n) = 5*a(n-1) + 10*a(n-2), with a(1)=0 and a(2)=1.
%H A180250 Nathaniel Johnston, <a href="/A180250/b180250.txt">Table of n, a(n) for n = 1..500</a>
%H A180250 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (5,10).
%F A180250 a(n) = ((5+sqrt(65))^(n-1) - (5-sqrt(65))^(n-1))/(2^(n-1)*sqrt(65)). - _Rolf Pleisch_, May 14 2011
%F A180250 G.f.: x^2/(1-5*x-10*x^2).
%F A180250 a(n) = (i*sqrt(10))^(n-1) * ChebyshevU(n-1, -i*sqrt(5/8)). - _G. C. Greubel_, Jul 21 2023
%t A180250 Join[{a=0,b=1},Table[c=5*b+10*a;a=b;b=c,{n,100}]]
%t A180250 LinearRecurrence[{5,10}, {0,1}, 30] (* _G. C. Greubel_, Jan 16 2018 *)
%o A180250 (PARI) a(n)=([0,1;10,5]^(n-1))[1,2] \\ _Charles R Greathouse IV_, Oct 03 2016
%o A180250 (PARI) my(x='x+O('x^30)); concat([0], Vec(x^2/(1-5*x-10*x^2))) \\ _G. C. Greubel_, Jan 16 2018
%o A180250 (Magma) [n le 2 select n-1 else 5*Self(n-1) +10*Self(n-2): n in [1..30]]; // _G. C. Greubel_, Jan 16 2018
%o A180250 (SageMath)
%o A180250 A180250= BinaryRecurrenceSequence(5,10,0,1)
%o A180250 [A180250(n-1) for n in range(1,41)] # _G. C. Greubel_, Jul 21 2023
%Y A180250 Cf. A001076, A006190, A007482, A015520, A015521, A015523, A015524, A015525, A015528, A015529, A015530, A015531, A015532, A015533, A015534, A015535, A015536, A015537, A015440, A015441, A015443, A015444, A015445, A015447, A030195, A053404, A057087, A057088, A083858, A085939, A090017, A091914, A099012, A180222, A180226.
%K A180250 nonn,easy
%O A180250 1,3
%A A180250 _Vladimir Joseph Stephan Orlovsky_, Jan 16 2011