A072945 Number of pairs (x,y) with x,y >= 0 such that x^3+y^2+x*y <= n.

1, 3, 3, 4, 5, 5, 5, 6, 7, 8, 8, 9, 9, 10, 10, 10, 12, 12, 12, 12, 12, 13, 13, 14, 14, 15, 15, 16, 16, 16, 16, 18, 19, 19, 19, 19, 20, 21, 21, 21, 21, 21, 21, 23, 23, 24, 24, 24, 24, 25, 25, 25, 25, 25, 25, 26, 27, 28, 28, 28, 28, 28, 28, 28, 30, 30, 30, 31, 31, 32, 32, 33, 33

Offset

0,2

Links

Table of n, a(n) for n=0..72.

Formula

Using Ikehara's theorem one can show that a(n) is asymptotic to C*n^(5/6) where C is a positive constant >0.7

Example

0^3 + 0^2 + 0*0, 0^3 + 1^2 + 0*1, 1^3 + 0^2 + 1*0 are 3 numbers <= 1 hence a(1) = 3.

Prog

(PARI) a(n)=sum(i=0, n, sum(j=0, n, if((sign(i^3+j^2+i*j-n)+1)*sign(i^3+j^2+i*j-n), 0, 1)))

Crossrefs

Sequence in context: A298200 A072648 A185585 * A307912 A274004 A196592

Adjacent sequences: A072942 A072943 A072944 * A072946 A072947 A072948

Keyword

nonn

Author

Benoit Cloitre, Aug 14 2002

Extensions

Name clarified by Sean A. Irvine, Nov 05 2024

Status

approved