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%I A286312 #12 May 16 2017 00:13:45
%S A286312 1,2,1,3,3,1,4,5,3,1,5,7,6,5,1,6,9,9,6,6,1,7,11,12,10,7,7,1,8,13,15,
%T A286312 14,10,7,8,1,9,15,18,18,15,11,7,9,1,10,17,21,22,20,15,12,17,10,1
%N A286312 Table read by antidiagonals upwards: a(n, k) is the minimum c such that n sets with k elements each can be constructed from numbers 1 to c (inclusive) such that any two sets have exactly 1 common element.
%H A286312 Simon Bohnen, <a href="https://github.com/Simonibo/dobble-generate/blob/master/values.xlsx">Extended table of values</a>
%H A286312 Simon Bohnen, <a href="https://github.com/Simonibo/dobble-generate/tree/master/src">A Java program for generating the sequence</a>
%H A286312 Simon Bohnen and other users, <a href="https://math.stackexchange.com/questions/2216585/what-is-the-minimal-number-of-different-symbols-in-the-game-dobble">Further discussion and proof for the formula</a>
%F A286312 n < k+2: a(n,k) = kn-(n(n-1))/2.
%e A286312 Top-left corner of the array:
%e A286312 1  1  1  1  1  1  ...
%e A286312 2  3  3  5  6  7  ...
%e A286312 3  5  6  6  7  7  ...
%e A286312 4  7  9  10 10 11 ...
%e A286312 5  9  12 14 15 15 ...
%e A286312 6  11 15 18 20 21 ...
%e A286312 :  :  :  :  :  : '.
%e A286312 For n=3 and k=3 the best possible solution is 6, the three sets are:
%e A286312 S1 = {1, 2, 3}
%e A286312 S2 = {1, 4, 5}
%e A286312 S3 = {2, 4, 6}
%K A286312 nonn,tabl
%O A286312 1,2
%A A286312 _Simon Bohnen_, May 06 2017

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