|
%I #9 Sep 08 2022 08:45:46
%S 3,30,306,3168,33156,349704,3708504,39476160,421307568,4504395744,
%T 48217133088,516565527552,5537243115072,59378264922240,
%U 636903805624704,6832763837309952,73311252232852224,786646960881163776
%N a(n) = 18*a(n-1) - 78*a(n-2) for n > 1; a(0) = 3, a(1) = 30.
%C Binomial transform of A163474. Inverse binomial transform of A163476.
%H G. C. Greubel, <a href="/A163475/b163475.txt">Table of n, a(n) for n = 0..965</a>
%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (18,-78).
%F a(n) = ((3+sqrt(3))*(9+sqrt(3))^n + (3-sqrt(3))*(9-sqrt(3))^n)/2.
%F G.f.: (3-24*x)/(1-18*x+78*x^2).
%F E.g.f.: exp(9*x)*( 3*cosh(sqrt(3)*x) + sqrt(3)*sinh(sqrt(3)*x) ). - _G. C. Greubel_, Jul 26 2017
%t LinearRecurrence[{18, -78}, {3, 30}, 50] (* _G. C. Greubel_, Jul 26 2017 *)
%o (Magma) [ n le 2 select 27*n-24 else 18*Self(n-1)-78*Self(n-2): n in [1..18] ];
%o (PARI) x='x+O('x^50); Vec((3-24*x)/(1-18*x+78*x^2)) \\ _G. C. Greubel_, Jul 26 2017
%Y Cf. A163474, A163476.
%K nonn
%O 0,1
%A _Klaus Brockhaus_, Aug 11 2009
| 