A215579 Integral averages of three distinct squares.

7, 10, 14, 15, 18, 22, 23, 25, 26, 27, 28, 30, 31, 35, 38, 39, 40, 42, 43, 46, 47, 49, 50, 51, 54, 55, 56, 57, 58, 60, 62, 63, 65, 66, 67, 70, 71, 72, 73, 74, 75, 78, 79, 81, 82, 83, 86, 87, 88, 90, 91, 92, 94, 95, 97, 98, 99, 100, 102, 103, 104, 105, 106

Offset

1,1

Comments

7 = (1^2 + 2^2 + 4^2)/3

10 = (1^2 + 2^2 + 5^2)/3

14 = (1^2 + 4^2 + 5^2)/3

First case with 2 ways: 23 = (1^2 + 2^2 + 8^2)/3 = (2^2 + 4^2 + 7^2)/3

42 has 3 sets of triples {a,b,c} such that 42= (a^2 + b^2 + c^2)/3: {1,2,11}, {1,5,10}, {3,6,9}

63 has 4 sets of triples {a,b,c}: {2,4,13}, {2,8,11}, {3,6,12}, {5,8,10}, etc.

Links

Zak Seidov, Table of n, a(n) for n = 1..1000

Mathematica

Take[Select[Mean/@Subsets[Range[20]^2, {3}], IntegerQ]//Union, 70] (* Harvey P. Dale, Aug 16 2016 *)

Crossrefs

Sequence in context: A178508 A123834 A064629 * A306469 A059752 A080205

Adjacent sequences: A215576 A215577 A215578 * A215580 A215581 A215582

Keyword

nonn

Author

Zak Seidov, Aug 16 2012

Status

approved