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A281864 Number of sets of exactly four positive integers <= n having a square element sum. 2
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

4,3

LINKS

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

EXAMPLE

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}.

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, 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 *)

CROSSREFS

Column k=4 of A281871.

Sequence in context: A261526 A295392 A023674 * A304025 A264395 A139218

Adjacent sequences:  A281861 A281862 A281863 * A281865 A281866 A281867

KEYWORD

nonn

AUTHOR

Alois P. Heinz, Feb 01 2017

STATUS

approved

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Last modified November 22 03:20 EST 2019. Contains 329383 sequences. (Running on oeis4.)