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A281868 Number of sets of exactly eight positive integers <= n having a square element sum.

%I A281868 #11 Feb 02 2017 19:13:27
%S A281868 1,1,3,13,34,86,197,405,786,1446,2532,4263,6938,10953,16837,25281,
%T A281868 37165,53605,75999,106075,145951,198199,265921,352825,463320,602609,
%U A281868 776797,993007,1259503,1585839,1983013,2463629,3042066,3734648,4559849,5538527,6694180
%N A281868 Number of sets of exactly eight positive integers <= n having a square element sum.
%H A281868 Alois P. Heinz, <a href="/A281868/b281868.txt">Table of n, a(n) for n = 8..1000</a>
%e A281868 a(8) = 1: {1,2,3,4,5,6,7,8}.
%e A281868 a(10) = 3: {1,2,3,4,5,6,7,8}, {1,3,5,6,7,8,9,10}, {2,3,4,6,7,8,9,10}.
%p A281868 b:= proc(n, i, t) option remember;
%p A281868       `if`(i<t, 0, `if`(n=0, `if`(t=0, 1, 0),
%p A281868       `if`(t<1 or n<t*(t+1)/2 or n>(t+1)*(2*i-t)/2, 0,
%p A281868       `if`(i>n, 0, b(n-i, i-1, t-1))+b(n, i-1, t))))
%p A281868     end:
%p A281868 a:= proc(n) option remember; `if`(n<0, 0, a(n-1)+add(
%p A281868        b(j^2-n, n-1, 7), j=isqrt(n-28)..isqrt(8*n-28)))
%p A281868     end:
%p A281868 seq(a(n), n=8..60);
%Y A281868 Column k=8 of A281871.
%K A281868 nonn
%O A281868 8,3
%A A281868 _Alois P. Heinz_, Feb 01 2017