%I #8 Oct 13 2022 17:31:51

%S 1,5,33,245,1889,14725,115137,901045,7053121,55213445,432231393,

%T 3383685365,26488919969,207366548485,1623353845377,12708307129525,

%U 99486055923841,778819338036485,6096930429659553,47729375549975285

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

%C Binomial transform of A084130.

%H G. C. Greubel, <a href="/A084131/b084131.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,-17).

%F a(n) = (5+sqrt(8))^n/2 + (5-sqrt(8))^n/2.

%F G.f.: (1-5*x)/(1-10*x+17*x^2).

%F E.g.f.: exp(5*x)*cosh(sqrt(8)*x).

%F 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 LinearRecurrence[{10,-17},{1,5},20] (* _Harvey P. Dale_, Apr 04 2021 *)

%o (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 (SageMath)

%o A084131=BinaryRecurrenceSequence(10,-17,1,5)

%o [A084131(n) for n in range(41)] # _G. C. Greubel_, Oct 13 2022

%Y Cf. A084130.

%K easy,nonn

%O 0,2

%A _Paul Barry_, May 16 2003