This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A217975 #56 Feb 14 2024 09:07:18
%S A217975 2,4,8,22,46,128,268,746,1562,4348,9104,25342,53062,147704,309268,
%T A217975 860882,1802546,5017588,10506008,29244646,61233502,170450288,
%U A217975 356895004,993457082,2080136522,5790292204,12123924128,33748296142,70663408246,196699484648
%N A217975 Integers k such that 2*k^2 - 7 is a square.
%C A217975 a(n) gives y-values solving the Diophantine equation x^2 + 7 = 2*y^2. A077446(n) gives the x-values. - _Sture Sjöstedt_, Oct 16 2012
%C A217975 Positive values of x (or y) satisfying x^2 - 6xy + y^2 + 28 = 0. - _Colin Barker_, Feb 08 2014
%H A217975 Vincenzo Librandi, <a href="/A217975/b217975.txt">Table of n, a(n) for n = 1..1000</a>
%H A217975 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (0,6,0,-1).
%F A217975 a(n) = 6*a(n - 2) - a(n - 4) with a(1)=2, a(2)=4, a(3)=8, a(4)=22. - _Sture Sjöstedt_, Oct 16 2012
%F A217975 a(n)*a(n+3)-a(n+1)*a(n+2) = 10-2*(-1)^n. - _Bruno Berselli_, Oct 25 2012
%F A217975 a(n) = 2*A006452(n). - _R. J. Mathar_, Oct 17 2012
%F A217975 G.f.: -2*x*(x - 1)*(x^2 + 3*x + 1)/((x^2 - 2*x - 1)*(x^2 + 2*x - 1)). - _Colin Barker_, Oct 24 2012
%F A217975 a(n) = a(-n+1) = ((4+sqrt(2))*(1-(-1)^n*sqrt(2))^(2*floor(n/2))+(4-sqrt(2))*(1+(-1)^n*sqrt(2))^(2*floor(n/2)))/4. - _Bruno Berselli_, Oct 25 2012
%F A217975 a(2n-1) = A078343(2n-1), a(2n) = A100525(n-1). - _Bruno Berselli_, Oct 25 2012
%e A217975 Since 2(4^2) - 7 = 25 = 5^2, and 4 is the second number with this property, a(2) = 4.
%t A217975 LinearRecurrence[{0, 6, 0, -1}, {2, 4, 8, 22}, 50] (* _Sture Sjöstedt_, Oct 16 2012 *)
%o A217975 (Magma) I:=[2, 4, 8, 22]; [n le 4 select I[n] else 6*Self(n-2)-Self(n-4): n in [1..31]]; // _Vincenzo Librandi_, Oct 16 2012
%o A217975 (PARI) Vec(2*x*(1-x)*(x^2+3*x+1)/(x^2-2*x-1)/(x^2+2*x-1)+O(x^99)) \\ _Charles R Greathouse IV_, Oct 24 2012
%Y A217975 Cf. A077442 (2*n^2 + 7 is a square).
%K A217975 nonn,easy
%O A217975 1,1
%A A217975 _Sture Sjöstedt_, Oct 16 2012