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A163460 a(n) = 16*a(n-1) - 62*a(n-2) for n > 1; a(0) = 1, a(1) = 9.

%I A163460 #10 Sep 08 2022 08:45:46
%S A163460 1,9,82,754,6980,64932,606152,5672648,53180944,499190928,4689836320,
%T A163460 44087543584,414630845504,3900665825856,36703540792448,
%U A163460 345415371476096,3251026414485760,30600669600254208,288047075905950208
%N A163460 a(n) = 16*a(n-1) - 62*a(n-2) for n > 1; a(0) = 1, a(1) = 9.
%C A163460 Binomial transform of A163459. Inverse binomial transform of A163461.
%H A163460 G. C. Greubel, <a href="/A163460/b163460.txt">Table of n, a(n) for n = 0..1000</a>
%H A163460 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (16, -62).
%F A163460 a(n) = ((2+sqrt(2))*(8+sqrt(2))^n + (2-sqrt(2))*(8-sqrt(2))^n)/4.
%F A163460 G.f.: (1-7*x)/(1-16*x+62*x^2).
%F A163460 E.g.f.: (1/2)*exp(8*x)*(2*cosh(sqrt(2)*x) + sqrt(2)*sinh(sqrt(2)*x)). - _G. C. Greubel_, Dec 24 2016
%t A163460 LinearRecurrence[{16,-62},{1,9},30] (* _Harvey P. Dale_, Jul 13 2014 *)
%o A163460 (Magma) [ n le 2 select 8*n-7 else 16*Self(n-1)-62*Self(n-2): n in [1..19] ];
%o A163460 (PARI) Vec((1-7*x)/(1-16*x+62*x^2) + O(x^50)) \\ _G. C. Greubel_, Dec 24 2016
%Y A163460 Cf. A163459, A163461.
%K A163460 nonn
%O A163460 0,2
%A A163460 _Klaus Brockhaus_, Jul 28 2009