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.

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

Offset

3,9

Comments

Terms computed by Michael Trott.

Links

Table of n, a(n) for n=3..57.

Eric Weisstein's World of Mathematics, Steffi Problem

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

T(b,b-1) gives A080203.

Sequence in context: A047938 A297481 A297533 * A300945 A234319 A224873

Adjacent sequences: A080199 A080200 A080201 * A080203 A080204 A080205

Keyword

nonn,tabl,base

Author

Eric W. Weisstein, Feb 05 2003

Status

approved