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A260896 a(n) gives the number of integers m such that there exist k and h with 2n^2 < mk^2 < 2(n+1)^2 and 2n^2 < 2mh^2 < 2(n+1)^2.

%I A260896 #13 Mar 24 2017 00:47:58
%S A260896 0,1,0,1,1,1,3,3,2,3,2,2,3,3,0,3,1,4,2,3,3,1,6,3,4,4,5,3,2,5,4,8,4,4,
%T A260896 5,1,5,6,4,5,3,6,2,5,7,5,8,4,7,4,7,7,7,10
%N A260896 a(n) gives the number of integers m such that there exist k and h with 2n^2 < mk^2 < 2(n+1)^2 and 2n^2 < 2mh^2 < 2(n+1)^2.
%C A260896 A072905(2n^2) > A006255(2n^2) and A066400(2n^2) > 2 for all n such that a(n) > 0.
%C A260896 Conjecture: a(n) > 0 for all n > 14.
%H A260896 Peter Kagey, <a href="/A260896/b260896.txt">Table of n, a(n) for n = 0..10000</a>
%e A260896 For n=12 the a(12)=3 solutions are 3, 6, and 37:
%e A260896   (1) (a) 2 * 12^2 <      3 * 10^2 < 2 * 13^2
%e A260896       (b) 2 * 12^2 < 2 *  3 *  7^2 < 2 * 13^2
%e A260896   (2) (a) 2 * 12^2 <      6 *  7^2 < 2 * 13^2
%e A260896       (b) 2 * 12^2 < 2 *  6 *  5^2 < 2 * 13^2
%e A260896   (3) (a) 2 * 12^2 <     37 *  3^2 < 2 * 13^2
%e A260896       (b) 2 * 12^2 < 2 * 37 *  2^2 < 2 * 13^2
%Y A260896 Cf. A006255, A066400, A072905.
%K A260896 nonn
%O A260896 0,7
%A A260896 _Peter Kagey_, Aug 03 2015