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A281866 Number of sets of exactly six positive integers <= n having a square element sum.

%I A281866 #9 Feb 02 2017 18:41:40
%S A281866 0,1,3,7,19,39,74,134,227,365,568,854,1247,1777,2479,3392,4562,6043,
%T A281866 7898,10194,13010,16428,20547,25474,31330,38248,46370,55846,66843,
%U A281866 79544,94161,110917,130044,151782,176391,204159,235410,270487,309744,353539,402255
%N A281866 Number of sets of exactly six positive integers <= n having a square element sum.
%H A281866 Alois P. Heinz, <a href="/A281866/b281866.txt">Table of n, a(n) for n = 6..1000</a>
%e A281866 a(7) = 1: {1,2,4,5,6,7}.
%e A281866 a(8) = 3: {1,2,3,4,7,8}, {1,2,3,5,6,8}, {1,2,4,5,6,7}.
%p A281866 b:= proc(n, i, t) option remember;
%p A281866       `if`(i<t, 0, `if`(n=0, `if`(t=0, 1, 0),
%p A281866       `if`(t<1 or n<t*(t+1)/2 or n>(t+1)*(2*i-t)/2, 0,
%p A281866       `if`(i>n, 0, b(n-i, i-1, t-1))+b(n, i-1, t))))
%p A281866     end:
%p A281866 a:= proc(n) option remember; `if`(n<0, 0, a(n-1)+add(
%p A281866        b(j^2-n, n-1, 5), j=isqrt(n-15)..isqrt(6*n-15)))
%p A281866     end:
%p A281866 seq(a(n), n=6..60);
%Y A281866 Column k=6 of A281871.
%K A281866 nonn
%O A281866 6,3
%A A281866 _Alois P. Heinz_, Feb 01 2017