A154025 - OEIS

%I #30 Jan 03 2024 23:46:55

%S 0,8,512,32760,2096128,134119432,8581547520,549084921848,

%T 35132853450752,2247953535926280,143833893445831168,

%U 9203121226997268472,588855924634379351040,37677576055373281198088,2410776011619255617326592

%N a(n+2) = 64*a(n+1) - a(n), a(1)=0, a(2)=8.

%C If a(n)=x and a(n+1)=y then (x^2+y^2)/(xy+1)=64.

%H Vincenzo Librandi, <a href="/A154025/b154025.txt">Table of n, a(n) for n = 1..200</a>

%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (64,-1).

%F G.f.: 8*x^2/(1 -64*x +x^2). - _R. J. Mathar_, Jan 05 2011

%t CoefficientList[Series[(8z)/(z^2-64z+1),{z,0,20}],z] (* _Vincenzo Librandi_, Jan 29 2012 *)

%t LinearRecurrence[{64,-1},{0,8},20] (* _Harvey P. Dale_, Dec 19 2023 *)

%o (Magma) I:=[0, 8]; [n le 2 select I[n] else 64*Self(n-1)-Self(n-2): n in [1..20]]; // _Vincenzo Librandi_, Jan 29 2012

%o (PARI) a(n)=([0,1; -1,64]^(n-1)*[0;8])[1,1] \\ _Charles R Greathouse IV_, Sep 01 2016

%Y Cf. A065100, A154021-A154027.

%K nonn,easy

%O 1,2

%A _Vincenzo Librandi_, Jan 04 2009