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%I #9 Sep 08 2022 08:45:46
%S 3,33,369,4179,47787,550377,6372201,74057451,863045523,10077337713,
%T 117831338529,1379125012419,16152860411067,189282082016697,
%U 2218814180460441,26015921653589211,305093457567121443
%N a(n) = 20*a(n-1) - 97*a(n-2) for n > 1; a(0) = 3, a(1) = 33.
%C Binomial transform of A163475. Tenth binomial transform of A056449.
%H G. C. Greubel, <a href="/A163476/b163476.txt">Table of n, a(n) for n = 0..930</a>
%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (20,-97).
%F a(n) = ((3+sqrt(3))*(10+sqrt(3))^n + (3-sqrt(3))*(10-sqrt(3))^n)/2.
%F G.f.: (3-27*x)/(1-20*x+97*x^2).
%F E.g.f.: exp(10*x)*( 3*cosh(sqrt(3)*x) + sqrt(3)*sinh(sqrt(3)*x) ). - _G. C. Greubel_, Jul 26 2017
%t LinearRecurrence[{20, -97}, {3, 33}, 50] (* _G. C. Greubel_, Jul 26 2017 *)
%o (Magma) [ n le 2 select 30*n-27 else 20*Self(n-1)-97*Self(n-2): n in [1..17] ];
%o (PARI) x='x+O('x^50); Vec((3-27*x)/(1-20*x+97*x^2)) \\ _G. C. Greubel_, Jul 26 2017
%Y Cf. A163475, A056449.
%K nonn,easy
%O 0,1
%A _Klaus Brockhaus_, Aug 11 2009
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