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A163414 a(n) = 16*a(n-1) - 62*a(n-2) for n>1, a(0)=1, a(1)=12.

%I A163414 #10 Jun 30 2023 00:57:11
%S A163414 1,12,130,1336,13316,130224,1257992,12053984,114868240,1090544832,
%T A163414 10326886432,97616403328,921595494464,8693310905088,81954053824640,
%U A163414 772279585078784,7275322024132864,68523818111241216,645311124283621888
%N A163414 a(n) = 16*a(n-1) - 62*a(n-2) for n>1, a(0)=1, a(1)=12.
%C A163414 Binomial transform of A163413. Inverse binomial transform of A163415.
%H A163414 G. C. Greubel, <a href="/A163414/b163414.txt">Table of n, a(n) for n = 0..1000</a>
%H A163414 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (16, -62).
%F A163414 a(n) = ((1+2*sqrt(2))*(8+sqrt(2))^n + (1-2*sqrt(2))*(8-sqrt(2))^n)/2.
%F A163414 G.f.: (1-4*x)/(1-16*x+62*x^2).
%F A163414 E.g.f.: exp(8*x)*( cosh(sqrt(2)*x) + 2*sqrt(2)*sinh(sqrt(2)*x) ). - _G. C. Greubel_, Dec 21 2016
%t A163414 LinearRecurrence[{16,-62}, {1,12}, 50] (* _G. C. Greubel_, Dec 21 2016 *)
%o A163414 (Magma) [n le 2 select 11*n-10 else 16*Self(n-1)-62*Self(n-2): n in [1..19]];
%o A163414 (PARI) Vec((1-4*x)/(1-16*x+62*x^2) + O(x^50)) \\ _G. C. Greubel_, Dec 21 2016
%Y A163414 Cf. A163413, A163415.
%K A163414 nonn,easy
%O A163414 0,2
%A A163414 _Klaus Brockhaus_, Jul 27 2009