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%I #31 Jan 15 2021 06:08:58
%S 1,1,3,3,3,3,4,4,5,4,5,5,5,6,6,6,6,6,6,7,7,7,7,7,8,7,8,8,8,8,8,9,8,9,
%T 9,9,9,9,9,9,10,10,9,10,10,10,11,10,11,10,11,10,11,11,11,12,11,11,12,
%U 11,12,12,12,12,12,12,12,12,13,12,13,12,13,13,13,13,13,13,14,13,14,13,14
%N Number of squares in (n^3, (n+1)^3 ].
%C There are never exactly two squares between two consecutive cubes. - _Vladimir Pletser_, Jan 12 2021
%H Vladimir Pletser, <a href="/A035936/b035936.txt">Table of n, a(n) for n = 0..10000</a>
%F a(n) = A000093(n+1)-A000093(n) (first differences of A000093). - _Henry Bottomley_, Aug 31 2000
%e a(3)=3 since 3^3 < 6^2, 7^2, 8^2 <= 4^3.
%p for n from 0 to 10000 do print(n, floor((n+1)^(3/2))-floor(n^(3/2))) end do; # _Vladimir Pletser_, Jan 11 2021
%t With[{sqs=Range[800]^2},Table[Count[sqs,_?(#>n^3&& #<=(n+1)^3&)],{n,0,85}]] (* _Harvey P. Dale_, Apr 12 2011 *)
%Y Cf. A000093, A000290 (squares), A000578 (cubes).
%K easy,nonn
%O 0,3
%A _Erich Friedman_
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