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

0,9

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).

Links

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

Formula

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

Example

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.

Prog

(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

Crossrefs

Cf. A000037, A004526, A087153.

Sequence in context: A087735 A322630 A277194 * A106250 A029248 A085916

Adjacent sequences: A172148 A172149 A172150 * A172152 A172153 A172154

Keyword

nonn,easy

Author

Reinhard Zumkeller, Jan 26 2010

Extensions

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

Status

approved