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 A172151 Number of partitions of n into two nonsquares. 6

%I

%S 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,

%T 11,11,13,12,13,13,13,13,15,15,15,15,16,17,17,17,18,18,19,18,20,20,20,

%U 20,21,21,23,22,23,24,24,24,25,26,25,25,27,26,27,27,28,29,30,29,30,30,31

%N Number of partitions of n into two nonsquares.

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

%H R. Zumkeller, <a href="/A172151/b172151.txt">Table of n, a(n) for n = 0..10000</a>

%F a(n) = n/2 + O(sqrt(n)). - _Charles R Greathouse IV_, Aug 28 2016

%e a(8) = #{6+2, 5+3} = 2;

%e a(9) = #{7+2, 6+3} = 2;

%e a(10) = #{8+2, 7+3, 5+5} = 3;

%e a(11) = #{8+3, 6+5} = 2;

%e a(12) = #{10+2, 7+5, 6+6} = 3;

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

%o (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

%Y Cf. A000037, A004526, A087153.

%K nonn,easy

%O 0,9

%A _Reinhard Zumkeller_, Jan 26 2010

%E Typo in b-file link fixed by _Reinhard Zumkeller_, Feb 10 2010

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Last modified January 20 14:40 EST 2019. Contains 319333 sequences. (Running on oeis4.)