

A318240


Triangle read by rows: T(n,k) = solution to Dagstuhl's Happy Diner Problem with n participants and tables of size at most k (n > k >= 2).


1



3, 3, 3, 5, 3, 3, 5, 4, 3, 3, 7, 4, 3, 3, 3, 7, 4, 3, 3, 3, 3, 9, 4, 4, 3, 3, 3, 3, 9, 6, 4, 4, 3, 3, 3, 3, 11, 6, 5, 4, 3, 3, 3, 3, 3, 11, 6, 5, 4, 3, 3, 3, 3, 3, 3, 13, 7, 5, 5, 4, 3, 3, 3, 3, 3, 3, 13, 7, 5, 5, 4, 4, 3, 3, 3, 3, 3, 3, 15, 7, 5, 5, 4, 4, 3
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OFFSET

3,1


COMMENTS

There are n participants at a conference, which share meals together in a room with multiple tables. Each table seats at most k participants. T(n,k) is the smallest number of meals so that each participants can share at least one meal with every other participant.
There is no requirement on the number of tables, participants can have a meal together more than once, and not every table needs to be fully occupied.
T(1,k) = 0 and T(n,k) = 1 for 1 < n <= k. These trivial values are omitted in this sequence.
Since every participant can sit with at most (k1) other participants, T(n,k) >= (n1)/(k1).
If A107431(n,k) * (k1) = n*k  2 then T(n * k, k) = A107431(n,k) + 1.


LINKS



EXAMPLE

The triangle begins as follows. The first entry is (n,k) = (3,2).
3
3 3
5 3 3
5 4 3 3
7 4 3 3 3
...
T(4,2) = 3 from the table assignment { 12/34, 13/24, 14/23 }


CROSSREFS



KEYWORD



AUTHOR



STATUS

approved



