cp's OEIS Frontend

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.

%I A322741 #7 Dec 24 2018 21:39:32
%S A322741 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,
%T A322741 33,34,39,42,43,44,45,46,48,49,50,51,54,56,58,59,64,66,67,70,73,80,87,
%U A322741 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
%N 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.
%C A322741 The sequence gives the areas multiplied by 2.
%C A322741 For more information see A322740.
%C A322741 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).
%o A322741 (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]))))
%o A322741 vecsort(abs(a))
%Y A322741 Cf. A303331, A322740, A322742.
%K A322741 nonn,fini,full
%O A322741 1,2
%A A322741 _Hugo Pfoertner_, Dec 24 2018