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%I #25 Dec 30 2014 13:12:13
%S 0,1,4,9,28,73,144,409,1036,2025,5716,14449,28224,79633,201268,393129,
%T 1109164,2803321,5475600,15448681,39045244,76265289,215172388,
%U 543830113,1062238464,2996964769,7574576356,14795073225,41742334396,105500238889,206068786704,581395716793,1469428768108
%N Values of y solving x^2 = floor(y^2/3 + y).
%C The corresponding values of x are given by A232771.
%C a(n) + 3 gives the values of y solving x^2 = floor(y^2/3 - y), and yields the same values for x.
%C a(3n+1) are squares whose square roots are given by A005320.
%C Let b(n) equal the second differences of a(n) where b(1) = 2. Then, for n>0, b(3n-1) = b(3n-2) = 2* A001570(n+1); b(3n)= 2*A011943(n); and b(3n) = (b(3n+1) + b(3n-1))/2.
%F Empirical g.f.: -x^2*(x+1)*(x^2+x+1)^2 / ((x-1)*(x^6-14*x^3+1)). - _Colin Barker_, Dec 30 2014
%o (PARI) is(n)=issquare(n^2\3+n)
%o print1("0, 1");for(x=3,99,y=round(sqrt(3)*x-3/2);if(is(y),print1(", "y))) \\ _Charles R Greathouse IV_, Dec 09 2013
%Y Cf. A005320, A011943, A001570, A110293.
%K nonn
%O 1,3
%A _Richard R. Forberg_, Nov 29 2013
%E a(23) corrected by _Colin Barker_, Dec 30 2014
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