A281864 Number of sets of exactly four positive integers <= n having a square element sum.

0, 0, 2, 5, 8, 14, 23, 34, 49, 69, 93, 123, 160, 204, 255, 315, 383, 462, 554, 658, 775, 904, 1046, 1205, 1384, 1581, 1797, 2031, 2282, 2556, 2857, 3183, 3535, 3913, 4316, 4748, 5211, 5706, 6235, 6798, 7393, 8025, 8696, 9406, 10159, 10956, 11793, 12673, 13599

Offset: 4

Author

Alois P. Heinz, Feb 01 2017

Keywords

• nonn

Examples

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

Links

• Alois P. Heinz, Table of n, a(n) for n = 4..4000

Crossrefs

Column k=4 of A281871.

Programs

Maple

b:= proc(n, i, t) option remember;
      `if`(i(t+1)*(2*i-t)/2, 0,
      `if`(i>n, 0, b(n-i, i-1, t-1))+b(n, i-1, t))))
    end:
a:= proc(n) option remember; `if`(n<0, 0, a(n-1)+add(
       b(j^2-n, n-1, 3), j=isqrt(n-6)..isqrt(4*n-6)))
    end:
seq(a(n), n=4..60);

Mathematica

Table[Count[Subsets[Range[n],{4}],?(IntegerQ[Sqrt[Total[#]]]&)],{n,4,60}] (* _Harvey P. Dale, Mar 06 2019 *)