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

5,3

Links

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

Example

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}.

Maple

b:= proc(n, i, t) option remember;
      `if`(i<t, 0, `if`(n=0, `if`(t=0, 1, 0),
      `if`(t<1 or n<t*(t+1)/2 or n>(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);

Crossrefs

Column k=5 of A281871.

Sequence in context: A283551 A362438 A000135 * A267698 A065220 A048094

Adjacent sequences: A281862 A281863 A281864 * A281866 A281867 A281868

Keyword

nonn

Author

Alois P. Heinz, Feb 01 2017

Status

approved