A035936 Number of squares in (n^3, (n+1)^3 ].

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

Vladimir Pletser, Table of n, a(n) for n = 0..10000

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

Adjacent sequences: A035933 A035934 A035935 * A035937 A035938 A035939

Keyword

easy,nonn

Author

Erich Friedman

Status

approved