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

0,2

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

Formula

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

Mathematica

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

Prog

(Haskell)
a144968 n = a144968_list !! n
a144968_list = zipWith (-) (tail a185549_list) a185549_list
-- Reinhard Zumkeller, Jul 24 2015
(PARI) for(n=0, 50, print1(ceil((n+1)^(3/2)) - ceil(n^(3/2)), ", ")) \\ G. C. Greubel, Jul 08 2017

Crossrefs

Cf. A000290, A000578, A077115.

Cf. A010052, A185549.

Sequence in context: A118653 A173753 A295753 * A239328 A076753 A352576

Adjacent sequences: A144965 A144966 A144967 * A144969 A144970 A144971

Keyword

nonn

Author

Reinhard Zumkeller, Sep 27 2008, Sep 29 2008

Status

approved