A144968 - OEIS

%I #13 Jul 08 2017 12:48:05

%S 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,

%T 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,

%U 11,12,12,12,11,13,12,12,12,13,12,13,12,13,13,13,13,13,13,14,13,13,14,14

%N Number of squares between consecutive cubes.

%C a(n) = sum {A010052(k): n^3 <= k < (n+1)^3}. - _Reinhard Zumkeller_, Jul 24 2015, corrected.

%H Reinhard Zumkeller, <a href="/A144968/b144968.txt">Table of n, a(n) for n = 0..10000</a>

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

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

%o (Haskell)

%o a144968 n = a144968_list !! n

%o a144968_list = zipWith (-) (tail a185549_list) a185549_list

%o -- _Reinhard Zumkeller_, Jul 24 2015

%o (PARI) for(n=0,50, print1(ceil((n+1)^(3/2)) - ceil(n^(3/2)), ", ")) \\ _G. C. Greubel_, Jul 08 2017

%Y Cf. A000290, A000578, A077115.

%Y Cf. A010052, A185549.

%K nonn

%O 0,2

%A _Reinhard Zumkeller_, Sep 27 2008, Sep 29 2008