A154022 - OEIS

%I #47 Mar 15 2024 02:22:50

%S 0,5,125,3120,77875,1943755,48516000,1210956245,30225390125,

%T 754423796880,18830369531875,470004814499995,11731289992968000,

%U 292812245009700005,7308574835249532125,182421558636228603120

%N a(n) = 5*A097780(n-2).

%C If a(n)=x and a(n+1)=y, then (x^2+y^2)/(xy+1)=25.

%H Vincenzo Librandi, <a href="/A154022/b154022.txt">Table of n, a(n) for n = 1..500</a>

%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (25,-1).

%F a(n) = +25*a(n-1) -a(n-2).

%F G.f.: 5*x^2/(1 -25*x +x^2). - _R. J. Mathar_, Jan 05 2011

%t CoefficientList[Series[(5*z)/(z^2-25*z+1),{z,0,25}],z] (* _Vincenzo Librandi_, Jan 29 2012 *)

%t LinearRecurrence[{25,-1},{0,5},20] (* _Harvey P. Dale_, Mar 06 2018 *)

%o (PARI) concat(0,Vec(5/(1-25*x+x^2)+O(x^98))) \\ _Charles R Greathouse IV_, Dec 27 2011

%o (Magma) I:=[0, 5]; [n le 2 select I[n] else 25*Self(n-1)-Self(n-2): n in [1..20]]; // _Vincenzo Librandi_, Jan 29 2012

%Y Cf. A065100, A154021-A154027.

%K nonn,easy

%O 1,2

%A _Vincenzo Librandi_, Jan 04 2009

%E Edited by _N. J. A. Sloane_, Jun 23 2010 at the suggestion of _Joerg Arndt_.