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%I #22 Jan 01 2024 11:38:17
%S 0,3,15,84,465,2577,14280,79131,438495,2429868,13464825,74613729,
%T 413463120,2291156787,12696173295,70354336836,389860204065,
%U 2160364030833,11971400766360,66338095924299,367604681920575
%N a(n) = 5*a(n-1) + 3*a(n-2), where a(0) = 0, a(1) = 3.
%H G. C. Greubel, <a href="/A106569/b106569.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 (5,3).
%F a(n) = 5*a(n-1) + 3*a(n-2), a(0) = 0, a(1) = 3.
%F a(n) = 3*A015536(n).
%F G.f.: 3*x/(1 - 5*x - 3*x^2). - _G. C. Greubel_, Sep 07 2021
%p a[0]:=0: a[1]:=3: for n from 2 to 23 do a[n]:= 5*a[n-1]+3*a[n-2] od: seq(a[n], n=0..23);
%t LinearRecurrence[{5,3}, {0,3}, 40] (* _G. C. Greubel_, Sep 07 2021 *)
%o (Magma) [n le 2 select 3*(n-1) else 5*Self(n-1) + 3*Self(n-2): n in [1..41]]; // _G. C. Greubel_, Sep 07 2021
%o (Sage) [3*lucas_number1(n,5,-3) for n in (0..40)] # _G. C. Greubel_, Sep 07 2021
%Y Cf. A015536.
%K nonn,easy,less
%O 0,2
%A _Roger L. Bagula_, May 30 2005
%E Edited by _N. J. A. Sloane_, Apr 30 2006
%E New (corrected) name by _G. C. Greubel_, Sep 07 2021
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