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A163412 a(n) = 12*a(n-1) - 34*a(n-2) for n>1, a(0)=1, a(1)=10.

%I A163412 #10 Sep 08 2022 08:45:46
%S A163412 1,10,86,692,5380,41032,309464,2318480,17299984,128771488,957058400,
%T A163412 7106470208,52737656896,391231895680,2901702413696,21518544511232,
%U A163412 159564652069120,1183145311447552,8772545567020544,65043606215029760
%N A163412 a(n) = 12*a(n-1) - 34*a(n-2) for n>1, a(0)=1, a(1)=10.
%C A163412 Binomial transform of A163349. Inverse binomial transform of A163413.
%H A163412 G. C. Greubel, <a href="/A163412/b163412.txt">Table of n, a(n) for n = 0..1000</a>
%H A163412 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (12,-34).
%F A163412 a(n) = ((1+2*sqrt(2))*(6+sqrt(2))^n + (1-2*sqrt(2))*(6-sqrt(2))^n)/2.
%F A163412 O.g.f.: (1 - 2*x)/(1 - 12*x + 34*x^2).
%F A163412 E.g.f.: exp(6*x)*( cosh(sqrt(2)*x) + 2*sqrt(2)*sinh(sqrt(2)*x) ). - _G. C. Greubel_, Dec 21 2016
%t A163412 LinearRecurrence[{12,-34}, {1,10}, 50] (* _G. C. Greubel_, Dec 21 2016 *)
%o A163412 (Magma) [n le 2 select 9*n-8 else 12*Self(n-1)-34*Self(n-2): n in [1..20]];
%o A163412 (PARI) Vec((1-2*x)/(1-12*x+34*x^2) + O(x^50)) \\ _G. C. Greubel_, Dec 21 2016
%Y A163412 Cf. A163349, A163413.
%K A163412 nonn,easy
%O A163412 0,2
%A A163412 _Klaus Brockhaus_, Jul 27 2009