A163460 - OEIS

%I #10 Sep 08 2022 08:45:46

%S 1,9,82,754,6980,64932,606152,5672648,53180944,499190928,4689836320,

%T 44087543584,414630845504,3900665825856,36703540792448,

%U 345415371476096,3251026414485760,30600669600254208,288047075905950208

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

%C Binomial transform of A163459. Inverse binomial transform of A163461.

%H G. C. Greubel, <a href="/A163460/b163460.txt">Table of n, a(n) for n = 0..1000</a>

%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (16, -62).

%F a(n) = ((2+sqrt(2))*(8+sqrt(2))^n + (2-sqrt(2))*(8-sqrt(2))^n)/4.

%F G.f.: (1-7*x)/(1-16*x+62*x^2).

%F 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 LinearRecurrence[{16,-62},{1,9},30] (* _Harvey P. Dale_, Jul 13 2014 *)

%o (Magma) [ n le 2 select 8*n-7 else 16*Self(n-1)-62*Self(n-2): n in [1..19] ];

%o (PARI) Vec((1-7*x)/(1-16*x+62*x^2) + O(x^50)) \\ _G. C. Greubel_, Dec 24 2016

%Y Cf. A163459, A163461.

%K nonn

%O 0,2

%A _Klaus Brockhaus_, Jul 28 2009