cp's OEIS Frontend

A172151 Number of partitions of n into two nonsquares.

%I A172151 #10 Aug 28 2016 03:31:27
%S A172151 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 A172151 11,11,13,12,13,13,13,13,15,15,15,15,16,17,17,17,18,18,19,18,20,20,20,
%U A172151 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 A172151 Number of partitions of n into two nonsquares.
%C A172151 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 A172151 R. Zumkeller, <a href="/A172151/b172151.txt">Table of n, a(n) for n = 0..10000</a>
%F A172151 a(n) = n/2 + O(sqrt(n)). - _Charles R Greathouse IV_, Aug 28 2016
%e A172151 a(8) = #{6+2, 5+3} = 2;
%e A172151 a(9) = #{7+2, 6+3} = 2;
%e A172151 a(10) = #{8+2, 7+3, 5+5} = 3;
%e A172151 a(11) = #{8+3, 6+5} = 2;
%e A172151 a(12) = #{10+2, 7+5, 6+6} = 3;
%e A172151 a(13) = #{11+2, 10+3, 8+5, 7+6} = 4.
%o A172151 (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 A172151 Cf. A000037, A004526, A087153.
%K A172151 nonn,easy
%O A172151 0,9
%A A172151 _Reinhard Zumkeller_, Jan 26 2010
%E A172151 Typo in b-file link fixed by _Reinhard Zumkeller_, Feb 10 2010