A355490 Numbers of the form a+b+c = a^2 - b^2 - c^2 where a > b >= c > 0.

8, 15, 20, 24, 27, 32, 35, 39, 44, 48, 49, 51, 54, 55, 56, 63, 64, 65, 68, 75, 80, 84, 87, 90, 92, 95, 98, 99, 104, 111, 114, 116, 119, 120, 123, 125, 128, 132, 135, 140, 143, 144, 147, 152, 153, 155, 159, 160, 164, 168, 170, 171, 174, 175, 176, 183, 184, 185, 188, 189, 195, 200, 203, 204, 207, 208, 209, 212, 215, 216, 219, 220, 224, 230, 231

Offset: 1

Author

Mohammad Arab, Jul 04 2022

Keywords

• nonn

Comments

It seems that A082867 is a subsequence.

The first counterexample to the above is A082867(60) = 258. - Charles R Greathouse IV, Jul 05 2022

Examples

			8 is a term: 8 = 4+2+2 = 4^2 - 2^2 - 2^2.
15 is a term: 15 = 7+5+3 = 7^2 - 5^2 - 3^2.
		

Links

• Charles R Greathouse IV, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A082867, A082772, A134582, A355491.

Programs

Mathematica

Solve[a==r^2-s^2-d^2 && 1<=r<=120 && 1<=s<=120 && 1<=d<=120 && 0<=a && r>s>=d && a==r+s+d, {a,r,s,d}, Integers]

PARI

list(lim)=my(v=List([8]));lim\=1;for(a=3,lim-2,my(a2=a^2);for(b=(sqrt(2*a^2+2*a+1)-1)\2,a-2,my(t=a2-b^2-a-b,s);if(issquare(4*t+1,&s) && (c=(s-1)/2)<=b && c<=b && a+b+c<=lim, listput(v,a+b+c)))); Set(v) \\ Charles R Greathouse IV, Jul 05 2022

Extensions

a(57) = 184 inserted by Charles R Greathouse IV, Jul 05 2022