%I A140074
%S A140074 1,1,1,0,1,0,1,1,0,1,1,1,0,1,1,0,1,0,0,1,1,1,0,0,0,1,1,1,1,0,0,1,0,1,1,
%T A140074 0,1,0,0,0,1,1,0,1,1,0,1,0,0,1,1,0,1,1,0,1,0,0,1,0,1,1,1,0,1,0,0,0,1,0,
%U A140074 1,0,1,1,1,1,0,0,1,0,0,1,1,0,1,1,1,1,0,0,1,0,0,1,0,1,1,1,1,0,1
%N A140074 Excess over the asymptote of the number of perfect squares between cubes.
%C A140074 There are always at least two squares between positive consecutive cubes, 
               starting with the perfect squares 1 and 4 between the perfect cubes 
               1 (included) and 8 (excluded).
%C A140074 The number of squares between the cube of n (included) and the cube of 
               n+1 (excluded) is always one of the two integers bracketing 3*sqrt(n)/
               2.
%C A140074 The number a(n) in the sequence is 0 if the correct count is the lower 
               number or 1 if the actual count is the higher number.
%H A140074 G. P. Michon, <a href="http://www.numericana.com/answer/numbers.htm#bits">
               A Sequence of Bits with Strange Statistics</a>.
%F A140074 a(n) = floor(sqrt((n+1)^3-1)) - ceiling(sqrt(n^3)) + 1 - floor(1.5 sqrt(n))
%e A140074 The sequence starts with a(0)=1 for n=0 because there is just one perfect 
               square (0) between the cube of 0 (included) and the cube of 1 (excluded).
%e A140074 This exceeds by a(0)=1 the asymptotic expression floor(1.5*sqrt(n)) for 
               the value n=0.
%Y A140074 Sequence in context: A092079 A139312 A071041 this_sequence A090174 A165556 
               A127243
%Y A140074 Adjacent sequences: A140071 A140072 A140073 this_sequence A140075 A140076 
               A140077
%K A140074 easy,nonn
%O A140074 0,1
%A A140074 Gerard P. Michon (g.michon(AT)att.net), May 06 2008