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A281867 Number of sets of exactly seven positive integers <= n having a square element sum.

%I A281867 #9 Feb 02 2017 18:43:30
%S A281867 0,0,4,10,25,60,124,238,435,750,1237,1973,3047,4574,6706,9624,13546,
%T A281867 18742,25533,34292,45469,59585,77238,99127,126048,158897,198713,
%U A281867 246663,304057,372374,453245,548479,660104,790372,941770,1117035,1319141,1551314,1817124
%N A281867 Number of sets of exactly seven positive integers <= n having a square element sum.
%H A281867 Alois P. Heinz, <a href="/A281867/b281867.txt">Table of n, a(n) for n = 7..1000</a>
%e A281867 a(9) = 4: {1,2,3,6,7,8,9}, {1,2,4,5,7,8,9}, {1,3,4,5,6,8,9}, {2,3,4,5,6,7,9}.
%p A281867 b:= proc(n, i, t) option remember;
%p A281867       `if`(i<t, 0, `if`(n=0, `if`(t=0, 1, 0),
%p A281867       `if`(t<1 or n<t*(t+1)/2 or n>(t+1)*(2*i-t)/2, 0,
%p A281867       `if`(i>n, 0, b(n-i, i-1, t-1))+b(n, i-1, t))))
%p A281867     end:
%p A281867 a:= proc(n) option remember; `if`(n<0, 0, a(n-1)+add(
%p A281867        b(j^2-n, n-1, 6), j=isqrt(n-21)..isqrt(7*n-21)))
%p A281867     end:
%p A281867 seq(a(n), n=7..60);
%Y A281867 Column k=7 of A281871.
%K A281867 nonn
%O A281867 7,3
%A A281867 _Alois P. Heinz_, Feb 01 2017