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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 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,2

LINKS

Table of n, a(n) for n=1..55.

Simon Bohnen, Extended table of values

Simon Bohnen, A Java program for generating the sequence

Simon Bohnen and other users, Further discussion and proof for the formula

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

Adjacent sequences:  A286309 A286310 A286311 * A286313 A286314 A286315

KEYWORD

nonn,tabl

AUTHOR

Simon Bohnen, May 06 2017

STATUS

approved

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Last modified June 29 14:46 EDT 2022. Contains 354913 sequences. (Running on oeis4.)