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A281869 Number of sets of exactly nine positive integers <= n having a square element sum.

%I A281869 #11 Feb 02 2017 19:11:50
%S A281869 0,1,3,14,47,121,296,660,1358,2646,4905,8704,14887,24649,39651,62175,
%T A281869 95286,143038,210732,305210,435195,611697,848494,1162662,1575195,
%U A281869 2111713,2803273,3687272,4808464,6220104,7985229,10178073,12885638,16209468,20267579,25196567
%N A281869 Number of sets of exactly nine positive integers <= n having a square element sum.
%H A281869 Alois P. Heinz, <a href="/A281869/b281869.txt">Table of n, a(n) for n = 9..1000</a>
%e A281869 a(10) = 1: {1,2,3,4,5,7,8,9,10}.
%e A281869 a(11) = 3: {1,2,3,4,5,6,7,10,11}, {1,2,3,4,5,6,8,9,11}, {1,2,3,4,5,7,8,9,10}.
%p A281869 b:= proc(n, i, t) option remember;
%p A281869       `if`(i<t, 0, `if`(n=0, `if`(t=0, 1, 0),
%p A281869       `if`(t<1 or n<t*(t+1)/2 or n>(t+1)*(2*i-t)/2, 0,
%p A281869       `if`(i>n, 0, b(n-i, i-1, t-1))+b(n, i-1, t))))
%p A281869     end:
%p A281869 a:= proc(n) option remember; `if`(n<0, 0, a(n-1)+add(
%p A281869        b(j^2-n, n-1, 8), j=isqrt(n-36)..isqrt(9*n-36)))
%p A281869     end:
%p A281869 seq(a(n), n=9..60);
%Y A281869 Column k=9 of A281871.
%K A281869 nonn
%O A281869 9,3
%A A281869 _Alois P. Heinz_, Feb 01 2017