A322741 Sorted list of 84 distinct triangle areas corresponding to the unique solution to the problem of placing 9 points on a grid rectangle of minimal area, such that all triangles formed by any 3 of the points have distinct areas > 0.

1, 3, 4, 6, 8, 9, 11, 12, 13, 15, 16, 17, 18, 19, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 33, 34, 39, 42, 43, 44, 45, 46, 48, 49, 50, 51, 54, 56, 58, 59, 64, 66, 67, 70, 73, 80, 87, 91, 92, 94, 95, 98, 99, 100, 104, 106, 107, 110, 113, 114, 116, 117, 121, 123, 127, 130, 132, 134, 139, 140, 141, 143, 145, 146, 148, 152, 156, 159, 161, 162, 168, 174, 178

Offset

1,2

Comments

The sequence gives the areas multiplied by 2.

For more information see A322740.

The coordinates of the 9 grid points on the minimal 18 X 11 rectangle are (0,3), (1,9), (2,0), (3,10), (4,11), (12,2), (17,11), (18,1), (18,4).

Links

Table of n, a(n) for n=1..84.

Prog

(PARI) X=[0, 1, 2, 3, 4, 12, 17, 18, 18]; Y=[3, 9, 0, 10, 11, 2, 11, 1, 4]; 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))

Crossrefs

Cf. A303331, A322740, A322742.

Sequence in context: A050849 A039008 A291322 * A161579 A276214 A285206

Adjacent sequences: A322738 A322739 A322740 * A322742 A322743 A322744

Keyword

nonn,fini,full

Author

Hugo Pfoertner, Dec 24 2018

Status

approved