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A084131 a(n) = 10*a(n-1) - 17*a(n-2), a(0) = 1, a(1) = 5.

%I A084131 #8 Oct 13 2022 17:31:51
%S A084131 1,5,33,245,1889,14725,115137,901045,7053121,55213445,432231393,
%T A084131 3383685365,26488919969,207366548485,1623353845377,12708307129525,
%U A084131 99486055923841,778819338036485,6096930429659553,47729375549975285
%N A084131 a(n) = 10*a(n-1) - 17*a(n-2), a(0) = 1, a(1) = 5.
%C A084131 Binomial transform of A084130.
%H A084131 G. C. Greubel, <a href="/A084131/b084131.txt">Table of n, a(n) for n = 0..1000</a>
%H A084131 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (10,-17).
%F A084131 a(n) = (5+sqrt(8))^n/2 + (5-sqrt(8))^n/2.
%F A084131 G.f.: (1-5*x)/(1-10*x+17*x^2).
%F A084131 E.g.f.: exp(5*x)*cosh(sqrt(8)*x).
%F A084131 a(n) = 17^((n-1)/2)*( sqrt(17)*ChebyshevU(n, 5/sqrt(17)) - 5*ChebyshevU(n-1, 5/sqrt(17)) ). - _G. C. Greubel_, Oct 13 2022
%t A084131 LinearRecurrence[{10,-17},{1,5},20] (* _Harvey P. Dale_, Apr 04 2021 *)
%o A084131 (Magma) [n le 2 select 5^(n-1) else 10*Self(n-1) -17*Self(n-2): n in [1..41]]; // _G. C. Greubel_, Oct 13 2022
%o A084131 (SageMath)
%o A084131 A084131=BinaryRecurrenceSequence(10,-17,1,5)
%o A084131 [A084131(n) for n in range(41)] # _G. C. Greubel_, Oct 13 2022
%Y A084131 Cf. A084130.
%K A084131 easy,nonn
%O A084131 0,2
%A A084131 _Paul Barry_, May 16 2003