A061266 - OEIS

%I #17 Jan 29 2023 21:01:49

%S 1,3,2,3,3,4,4,4,4,5,5,5,6,6,5,6,6,6,7,7,7,7,7,7,7,8,8,8,8,8,9,8,9,9,

%T 8,9,9,9,9,10,10,9,10,10,10,11,10,10,10,11,10,11,11,11,12,11,11,12,11,

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

%N Number of squares between n^3 and (n+1)^3.

%H Harry J. Smith, <a href="/A061266/b061266.txt">Table of n, a(n) for n = 1..2000</a>

%F a(n) = 3 if n=2; floor(sqrt((n+1)^3 - 1)) - floor(sqrt(n^3+1)) otherwise. - _Ralf Stephan_, Mar 28 2003 [Corrected by _Sean A. Irvine_, Jan 29 2023]

%e a(2) = 3 as there are three squares (9, 16 and 25) between 8 and 27.

%e a(3)= 2 as there are two squares (36 and 49) between 27 and 64. (64 is not counted, as it is not strictly between 27 and 64.)

%t a[1] = 1; a[2] = 3; a[n_] := Floor[Sqrt[(n+1)^3-1]] - Floor[Sqrt[n^3+1]]; Array[a, 100] (* _Jean-François Alcover_, Dec 04 2015, adapted from PARI *)

%o (PARI) print1("1,3,"):for(n=3,100,print1(sqrtint((n+1)^3-1)-sqrtint(n^3+1)","))

%o (PARI) { for (n=1, 2000, a=sqrtint((n+1)^3-1)-sqrtint(n^3+1); if (n==2, a=3); write("b061266.txt", n, " ", a); ) } \\ _Harry J. Smith_, Jul 20 2009

%K nonn

%O 1,2

%A _Amarnath Murthy_, Apr 24 2001

%E More terms from _Ralf Stephan_, Mar 28 2003

%E Offset changed from 0 to 1 by _Harry J. Smith_, Jul 20 2009