A281868 - OEIS

%I #11 Feb 02 2017 19:13:27

%S 1,1,3,13,34,86,197,405,786,1446,2532,4263,6938,10953,16837,25281,

%T 37165,53605,75999,106075,145951,198199,265921,352825,463320,602609,

%U 776797,993007,1259503,1585839,1983013,2463629,3042066,3734648,4559849,5538527,6694180

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

%H Alois P. Heinz, <a href="/A281868/b281868.txt">Table of n, a(n) for n = 8..1000</a>

%e a(8) = 1: {1,2,3,4,5,6,7,8}.

%e 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 b:= proc(n, i, t) option remember;

%p       `if`(i<t, 0, `if`(n=0, `if`(t=0, 1, 0),

%p       `if`(t<1 or n<t*(t+1)/2 or n>(t+1)*(2*i-t)/2, 0,

%p       `if`(i>n, 0, b(n-i, i-1, t-1))+b(n, i-1, t))))

%p     end:

%p a:= proc(n) option remember; `if`(n<0, 0, a(n-1)+add(

%p        b(j^2-n, n-1, 7), j=isqrt(n-28)..isqrt(8*n-28)))

%p     end:

%p seq(a(n), n=8..60);

%Y Column k=8 of A281871.

%K nonn

%O 8,3

%A _Alois P. Heinz_, Feb 01 2017