A322742 Sorted list of 120 distinct triangle areas corresponding to the unique solution to the problem of placing 10 points on a grid rectangle of minimal area, such that all triangles formed by any 3 of the points have distinct areas > 0.

1, 2, 3, 4, 7, 8, 9, 14, 15, 19, 20, 21, 23, 24, 26, 27, 28, 30, 31, 33, 34, 35, 36, 37, 39, 40, 42, 43, 45, 46, 47, 49, 50, 52, 53, 55, 56, 58, 59, 61, 65, 67, 68, 69, 70, 74, 75, 77, 78, 79, 80, 81, 84, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 100, 101, 106, 107, 111

Offset: 1

Author

Hugo Pfoertner, Dec 24 2018

Keywords

• nonn
• fini
• full

Comments

The sequence gives the areas multiplied by 2.

For more information see A322740.

The coordinates of the 10 grid points on the minimal 19 X 18 rectangle are (0,3), (1,9), (2,18), (5,0), (5,10), (12,17), (15,13), (17,4), (18,0), (19,5).

Links

• Hugo Pfoertner, Table of n, a(n) for n = 1..120

Crossrefs

Cf. A303331, A322740, A322741.

Programs

PARI

X=[0,1,2,5,5,12,15,17,18,19];Y=[3,9,18,0,10,17,13,4,0,5];n=0;a=vector(binomial(#X,3));for(i=1,#X-2,for(j=i+1,#X-1,for(k=j+1,#X,a[n++]=X[i]*(Y[j]-Y[k])+X[j]*(Y[k]-Y[i])+X[k]*(Y[i]-Y[j]))))
vecsort(abs(a))