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A198774 Numbers having exactly three representations by the quadratic form x^2+xy+y^2 with 0<=x<=y.

%I A198774 #11 Jun 21 2018 10:32:37
%S A198774 637,931,1183,1519,1813,1911,2107,2401,2527,2548,2793,2989,3211,3283,
%T A198774 3549,3577,3724,3871,4557,4693,4732,4753,5047,5239,5341,5439,5733,
%U A198774 6076,6223,6253,6321,6727,6811,7203,7252,7267,7399,7581,7644,7693,7987,8379,8428
%N A198774 Numbers having exactly three representations by the quadratic form x^2+xy+y^2 with 0<=x<=y.
%C A198774 A088534(a(n)) = 3; subsequence of A118886, see also A003136.
%H A198774 Reinhard Zumkeller, <a href="/A198774/b198774.txt">Table of n, a(n) for n = 1..1000</a>
%e A198774 a(1) = 637 = 4^2+4*23+23^2 = 7^2+7*21+21^2 = 12^2+12*17+17^2, A088534(637)=3;
%e A198774 a(2) = 931 = 1^2+1*30+30^2 = 9^2+9*25+25^2 = 14^2+14*21+21^2, A088534(273)=3.
%t A198774 amax = 10000; xmax = Sqrt[amax] // Ceiling; Clear[f]; f[_] = 0; Do[q = x^2 + x y + y^2; f[q] = f[q] + 1, {x, 0, xmax}, {y, x, xmax}];
%t A198774 A198774 = Select[Range[0, 3 xmax^2], # <= amax && f[#] == 3&] (* _Jean-François Alcover_, Jun 21 2018 *)
%o A198774 (Haskell)
%o A198774 a198774 n = a198774_list !! (n-1)
%o A198774 a198774_list = filter ((== 3) . a088534) a003136_list
%Y A198774 Cf. A198772, A198773, A198775.
%K A198774 nonn
%O A198774 1,1
%A A198774 _Reinhard Zumkeller_, Oct 30 2011