A281865 Number of sets of exactly five positive integers <= n having a square element sum.

0, 1, 2, 6, 13, 24, 43, 71, 110, 166, 242, 341, 469, 633, 838, 1091, 1400, 1774, 2219, 2745, 3364, 4089, 4933, 5904, 7015, 8279, 9713, 11338, 13172, 15230, 17524, 20071, 22895, 26025, 29485, 33294, 37472, 42040, 47026, 52463, 58383, 64816, 71785, 79318, 87444

Offset: 5

Author

Alois P. Heinz, Feb 01 2017

Keywords

• nonn

Examples

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

Links

• Alois P. Heinz, Table of n, a(n) for n = 5..1000

Crossrefs

Column k=5 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, 4), j=isqrt(n-10)..isqrt(5*n-10)))
    end:
seq(a(n), n=5..60);