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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.

%I A322742 #11 Dec 25 2018 02:50:04
%S A322742 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,
%T A322742 40,42,43,45,46,47,49,50,52,53,55,56,58,59,61,65,67,68,69,70,74,75,77,
%U A322742 78,79,80,81,84,89,90,91,92,93,94,95,96,97,98,100,101,106,107,111
%N 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.
%C A322742 The sequence gives the areas multiplied by 2.
%C A322742 For more information see A322740.
%C A322742 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).
%H A322742 Hugo Pfoertner, <a href="/A322742/b322742.txt">Table of n, a(n) for n = 1..120</a>
%o A322742 (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]))))
%o A322742 vecsort(abs(a))
%Y A322742 Cf. A303331, A322740, A322741.
%K A322742 nonn,fini,full
%O A322742 1,2
%A A322742 _Hugo Pfoertner_, Dec 24 2018