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Number of sets of exactly n positive integers <= n+6 having a square element sum.
2

%I #8 Aug 21 2017 17:18:39

%S 1,2,5,11,23,43,74,124,197,296,434,627,875,1188,1600,2128,2755,3522,

%T 4511,5661,6983,8637,10610,12781,15343,18497,21937,25751,30416,35702,

%U 41266,47772,55531,63578,72405,83101,94662,106544,120507,136663,152742,170490,191873

%N Number of sets of exactly n positive integers <= n+6 having a square element sum.

%H Alois P. Heinz, <a href="/A281969/b281969.txt">Table of n, a(n) for n = 0..1000</a>

%F a(n) = A281871(n+6,n).

%e a(4) = 23: {1,2,3,10}, {1,2,4,9}, {1,2,5,8}, {1,2,6,7}, {1,3,4,8}, {1,3,5,7}, {1,4,5,6}, {1,5,9,10}, {1,6,8,10}, {1,7,8,9}, {2,3,4,7}, {2,3,5,6}, {2,4,9,10}, {2,5,8,10}, {2,6,7,10}, {2,6,8,9}, {3,4,8,10}, {3,5,7,10}, {3,5,8,9}, {3,6,7,9}, {4,5,6,10}, {4,5,7,9}, {4,6,7,8}.

%t Table[Count[Subsets[Range[n+6],{n}],_?(IntegerQ[Sqrt[Total[#]]]&)],{n,0,50}] (* _Harvey P. Dale_, Aug 21 2017 *)

%Y A diagonal of A281871.

%K nonn

%O 0,2

%A _Alois P. Heinz_, Feb 03 2017