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A163473 a(n) = 14*a(n-1) - 46*a(n-2) for n > 1; a(0) = 3, a(1) = 24.

%I A163473 #9 Sep 08 2022 08:45:46
%S A163473 3,24,198,1668,14244,122688,1062408,9230064,80350128,700318848,
%T A163473 6108357984,53302344768,465248359488,4061569173504,35460543892608,
%U A163473 309615432515328,2703431036154624,23605724610459648,206122316883322368
%N A163473 a(n) = 14*a(n-1) - 46*a(n-2) for n > 1; a(0) = 3, a(1) = 24.
%C A163473 Binomial transform of A163472. Inverse binomial transform of A163474.
%H A163473 G. C. Greubel, <a href="/A163473/b163473.txt">Table of n, a(n) for n = 0..1000</a>
%H A163473 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (14,-46).
%F A163473 a(n) = ((3+sqrt(3))*(7+sqrt(3))^n + (3-sqrt(3))*(7-sqrt(3))^n)/2.
%F A163473 G.f.: (3-18*x)/(1-14*x+46*x^2).
%F A163473 E.g.f.: exp(7*x)*( 3*cosh(sqrt(3)*x) + sqrt(3)*sinh(sqrt(3)*x) ). - _G. C. Greubel_, Jul 26 2017
%t A163473 LinearRecurrence[{14, -46}, {3, 24}, 50] (* _G. C. Greubel_, Jul 26 2017 *)
%o A163473 (Magma) [ n le 2 select 21*n-18 else 14*Self(n-1)-46*Self(n-2): n in [1..19] ];
%o A163473 (PARI) x='x+O('x^50); Vec((3-18*x)/(1-14*x+46*x^2)) \\ _G. C. Greubel_, Jul 26 2017
%Y A163473 Cf. A163472, A163474.
%K A163473 nonn
%O A163473 0,1
%A A163473 _Klaus Brockhaus_, Aug 11 2009