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 A145525 Numbers X such that there exists Y in N : X^2=273*Y^2+91. 1

%I #18 Jan 03 2024 23:45:42

%S 182,264446,384504302,559068990662,812885927918246,

%T 1181935580124139022,1718533520614570219742,2498746557038004975365846,

%U 3633175775399738619611720342,5282635078684662914910466011422,7680947771231724478541197968887246

%N Numbers X such that there exists Y in N : X^2=273*Y^2+91.

%H Vincenzo Librandi, <a href="/A145525/b145525.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 (1454,-1).

%F a(n+2) = 1454*a(n+1)-a(n).

%F G.f.: -182*x*(x-1) / (x^2-1454*x+1). - _Colin Barker_, Oct 21 2014

%e a(1)=182 because the first relation is 182^2=273*11^2+91.

%t LinearRecurrence[{1454,-1},{182,264446},20] (* _Harvey P. Dale_, Nov 03 2012 *)

%t CoefficientList[Series[182 (1 - x)/(x^2 - 1454 x + 1), {x, 0, 20}], x] (* _Vincenzo Librandi_, Oct 21 2014 *)

%o (PARI) Vec(-182*x*(x-1)/(x^2-1454*x+1) + O(x^20)) \\ _Colin Barker_, Oct 21 2014

%o (Magma) I:=[182,264446]; [n le 2 select I[n] else 1454*Self(n-1)-Self(n-2): n in [1..15]]; // _Vincenzo Librandi_, Oct 21 2014

%K easy,nonn

%O 1,1

%A _Richard Choulet_, Oct 12 2008

%E Editing from _Colin Barker_, Oct 21 2014

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Last modified August 7 12:22 EDT 2024. Contains 375012 sequences. (Running on oeis4.)