A144968 Number of squares between consecutive cubes.

1, 2, 3, 2, 4, 3, 4, 4, 4, 5, 5, 5, 5, 6, 6, 5, 7, 6, 6, 7, 7, 7, 7, 7, 7, 8, 8, 8, 8, 8, 8, 9, 8, 9, 9, 8, 10, 9, 9, 9, 10, 10, 9, 10, 10, 10, 11, 10, 10, 11, 11, 10, 11, 11, 11, 12, 11, 11, 12, 11, 12, 12, 12, 11, 13, 12, 12, 12, 13, 12, 13, 12, 13, 13, 13, 13, 13, 13, 14, 13, 13, 14, 14

Offset: 0

Author

Reinhard Zumkeller, Sep 27 2008, Sep 29 2008

Keywords

• nonn

Comments

a(n) = sum {A010052(k): n^3 <= k < (n+1)^3}. - Reinhard Zumkeller, Jul 24 2015, corrected.

Links

• Reinhard Zumkeller, Table of n, a(n) for n = 0..10000

Crossrefs

Cf. A000290, A000578, A077115.

Cf. A010052, A185549.

Programs

Haskell

a144968 n = a144968_list !! n
a144968_list = zipWith (-) (tail a185549_list) a185549_list
-- Reinhard Zumkeller, Jul 24 2015

Mathematica

Last[#]-First[#]&/@Partition[Table[Ceiling[n^(3/2)],{n,0,90}],2,1] (* Harvey P. Dale, Jul 10 2013 *)

PARI

for(n=0,50, print1(ceil((n+1)^(3/2)) - ceil(n^(3/2)), ", ")) \\ G. C. Greubel, Jul 08 2017

Formula

a(n) = ceiling((n+1)^(3/2)) - ceiling(n^(3/2)).