%I #14 Feb 08 2015 04:35:57
%S 0,2,11,12,70,408,2378,13860,80782,470832,2744210,15994428,93222358,
%T 543339720,3166815962,18457556052,107578520350,627013566048,
%U 3654502875938,21300003689580,124145519261542,723573111879672,4217293152016490,24580185800219268
%N Numbers n such that 2*n^2+1 is a perfect power.
%C The value of y in the solution of the Diophantine equation x^a - 2*y^b = 1. All solutions have b=2. Sequence A075114 gives n^2. The only known solution for a>2 is y=11. See A075114 for more details.
%F Conjecture: a(n) = 6*a(n-1) - a(n-2) for n>5; g.f.: x^2*(2-x-52*x^2+9*x^3)/ (1-6*x+x^2). - _Colin Barker_, Apr 28 2012
%o (PARI)
%o Vec(x^2*(2-x-52*x^2+9*x^3)/ (1-6*x+x^2) + O(x^66))
%o /* _Joerg Arndt_, Apr 28 2012, using _Colin Barker_'s g.f. */
%K nonn
%O 1,2
%A _T. D. Noe_, Mar 29 2006
%E More terms from _T. D. Noe_, Nov 19 2006