A172151 Number of partitions of n into two nonsquares.

0, 0, 0, 0, 1, 1, 1, 1, 2, 2, 3, 2, 3, 4, 4, 4, 5, 5, 5, 5, 7, 6, 7, 7, 8, 9, 9, 8, 9, 10, 10, 10, 11, 11, 13, 12, 13, 13, 13, 13, 15, 15, 15, 15, 16, 17, 17, 17, 18, 18, 19, 18, 20, 20, 20, 20, 21, 21, 23, 22, 23, 24, 24, 24, 25, 26, 25, 25, 27, 26, 27, 27, 28, 29, 30, 29, 30, 30, 31

Offset: 0

Author

Reinhard Zumkeller, Jan 26 2010

Keywords

• nonn
• easy

Comments

A172152 and A172153 give record values and where they occur: a(A172153(n))=A172152(n) and a(m) < A172152(n) for m < A172153(n).

Examples

			a(8) = #{6+2, 5+3} = 2;
a(9) = #{7+2, 6+3} = 2;
a(10) = #{8+2, 7+3, 5+5} = 3;
a(11) = #{8+3, 6+5} = 2;
a(12) = #{10+2, 7+5, 6+6} = 3;
a(13) = #{11+2, 10+3, 8+5, 7+6} = 4.
		

Links

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

Crossrefs

Cf. A000037, A004526, A087153.

Programs

PARI

a(n)=n\2 - sqrtint(n) + sum(k=sqrtint(n\2)+1,sqrtint(n), issquare(n-k^2)) \\ Charles R Greathouse IV, Aug 28 2016

Formula

a(n) = n/2 + O(sqrt(n)). - Charles R Greathouse IV, Aug 28 2016

Extensions

Typo in b-file link fixed by Reinhard Zumkeller, Feb 10 2010