

A080202


Triangle T(b,k) read by rows, giving numbers of pairs of unequal permutations of all the digits 1, ..., k in base b (k<b) whose ratio is an integer.


1



0, 0, 1, 0, 0, 1, 0, 0, 3, 25, 0, 0, 0, 2, 7, 0, 0, 0, 0, 68, 623, 0, 0, 0, 0, 0, 124, 1183, 0, 0, 0, 0, 0, 0, 2338, 24603, 0, 0, 0, 0, 0, 0, 3, 598, 5895, 0, 0, 0, 0, 0, 0, 0, 0, 161947, 2017603
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OFFSET

3,9


COMMENTS

Terms computed by Michael Trott.


LINKS



EXAMPLE

Triangle is arranged as (b,k) = (3, 2), (4, 2), (4, 3), (5, 2), (5, 3), (5,4), (6,2), ....
In base 3, there are no solutions for 12, so T(3,2)=0. In base 4, there are no solutions for 12, so T(4,2)=0 and a single solution for 123, so T(4,3)=1. In base 5, there are no solutions with the digits 12 or 123, so T(5,1)=T(5,2)=0, but there is a single solution with the digits 1234: 4312_5/1234_5 = 3, so T(5,3)=1.
0;
0, 1;
0, 0, 1;
0, 0, 3, 25;
0, 0, 0, 2, 7;
0, 0, 0, 0, 68, 623;
0, 0, 0, 0, 0, 124, 1183;


CROSSREFS



KEYWORD



AUTHOR



STATUS

approved



