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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.
0
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, 14, 10, 7, 8, 1, 9, 15, 18, 18, 15, 11, 7, 9, 1, 10, 17, 21, 22, 20, 15, 12, 17, 10, 1
OFFSET
1,2
FORMULA
n < k+2: a(n,k) = kn-(n(n-1))/2.
EXAMPLE
Top-left corner of the array:
1 1 1 1 1 1 ...
2 3 3 5 6 7 ...
3 5 6 6 7 7 ...
4 7 9 10 10 11 ...
5 9 12 14 15 15 ...
6 11 15 18 20 21 ...
: : : : : : '.
For n=3 and k=3 the best possible solution is 6, the three sets are:
S1 = {1, 2, 3}
S2 = {1, 4, 5}
S3 = {2, 4, 6}
CROSSREFS
Sequence in context: A117895 A188002 A186974 * A278492 A128139 A208721
KEYWORD
nonn,tabl
AUTHOR
Simon Bohnen, May 06 2017
STATUS
approved