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A281064 Values of x such that x^2 = 5*y^2 + 11, where x and y are positive integers. 1

%I

%S 4,16,56,284,1004,5096,18016,91444,323284,1640896,5801096,29444684,

%T 104096444,528363416,1867934896,9481096804,33518731684,170131379056,

%U 601469235416,3052883726204,10792927505804,54781775692616,193671225869056,983019078740884

%N Values of x such that x^2 = 5*y^2 + 11, where x and y are positive integers.

%C The corresponding values of y are in A082651.

%H Colin Barker, <a href="/A281064/b281064.txt">Table of n, a(n) for n = 1..1000</a>

%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (0,18,0,-1).

%F a(n) = ((-2-r)^n*(r-5) + (5+r)*(r-2)^n + (15+7*r)*(r+2)^n + (2-r)^n*(7*r-15)) / (4*r) where r=sqrt(5).

%F a(n) = 18*a(n-2) - a(n-4) for n>3.

%F G.f.: 4*x*(1 - x)*(1 + 5*x + x^2) / ((1 + 4*x - x^2)*(1 - 4*x - x^2)).

%e 56 is in the sequence because 56^2 = 3136 = 5*25^2+11.

%t LinearRecurrence[{0,18,0,-1},{4,16,56,284},30] (* _Harvey P. Dale_, May 28 2020 *)

%o (PARI) Vec(4*x*(1 - x)*(1 + 5*x + x^2) / ((1 + 4*x - x^2)*(1 - 4*x - x^2)) + O(x^30))

%Y Cf. A082651.

%K nonn,easy

%O 1,1

%A _Colin Barker_, Jan 14 2017

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Last modified January 18 20:41 EST 2022. Contains 350455 sequences. (Running on oeis4.)