|
%I #22 Jan 05 2016 19:00:33
%S 0,3,5,32,203,333,2112,13395,21973,139360,883867,1449885,9195648,
%T 58321827,95670437,606773408,3848356715,6312798957,40037849280,
%U 253933221363,416549060725,2641891279072,16755744253243,27485925208893,174324786569472,1105625187492675
%N x-values in the solution to 17*x^2 + 16 = y^2.
%C When are both n-1 and 17*n-1 perfect squares? This problem gives the equation 17*x^2+16=y^2.
%H <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (0,0,66,0,0,-1).
%F a(n) = 66*a(n-3) - a(n-6), a(1)=0, a(2)=3, a(3)=5, a(4)=32, a(5)=203, a(6)=333.
%F G.f.: x^2*(3*x^4+5*x^3+32*x^2+5*x+3) / (x^6-66*x^3+1). - _Colin Barker_, Sep 01 2013
%e a(7)=66*32-0=2112.
%t LinearRecurrence[{0,0,66,0,0,-1}, {0,3,5,32,203,333}, 50]
%o (PARI) Vec(x^2*(3*x^4+5*x^3+32*x^2+5*x+3)/(x^6-66*x^3+1) + O(x^100)) \\ _Colin Barker_, Sep 01 2013
%Y Cf. A199772, A199773, A199798.
%K nonn,easy
%O 1,2
%A _Sture Sjöstedt_, Nov 10 2011
%E More terms from _T. D. Noe_, Nov 10 2011
|
