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.

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

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