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A035936
Number of squares in (n^3, (n+1)^3 ].
1
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, 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, 11, 12, 12, 12, 12, 12, 12, 12, 12, 13, 12, 13, 12, 13, 13, 13, 13, 13, 13, 14, 13, 14, 13, 14
OFFSET
0,3
COMMENTS
There are never exactly two squares between two consecutive cubes. - Vladimir Pletser, Jan 12 2021
LINKS
FORMULA
a(n) = A000093(n+1)-A000093(n) (first differences of A000093). - Henry Bottomley, Aug 31 2000
EXAMPLE
a(3)=3 since 3^3 < 6^2, 7^2, 8^2 <= 4^3.
MAPLE
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
MATHEMATICA
With[{sqs=Range[800]^2}, Table[Count[sqs, _?(#>n^3&& #<=(n+1)^3&)], {n, 0, 85}]] (* Harvey P. Dale, Apr 12 2011 *)
CROSSREFS
Cf. A000093, A000290 (squares), A000578 (cubes).
Sequence in context: A309555 A262994 A179847 * A006671 A046074 A328914
KEYWORD
easy,nonn
STATUS
approved