A158345 The number of pairs of independent outcomes when rolling an n-sided die. Or in other words, the number of pairs of proper subsets A,B of a set S, such that #A/#S * #B/#S = #(A \intersect B)/#S.

1, 5, 13, 53, 61, 845, 253, 7509, 16141, 128045, 4093, 1785965, 16381, 23576285, 55921333, 274696789, 262141, 5338300157, 1048573, 63028146573, 117924207421, 995274180125, 16777213, 15265519672173, 14283159085861

Offset

1,2

Links

Table of n, a(n) for n=1..25.

wwu riddle forum thread on the problem

Example

For N=4 we have 53 solutions, because {1,2,3,4} together with any proper subset yields 2*15-1 = 29 valid pairs, and a further 24 pairs can be obtained from {1,2} & {1,3}, by substituting the numbers with any permutation of (1,2,3,4).

Mathematica

Sum[Total[s!/(c!(#-c)!(s c/#-c)!(s - # - s c/# + c)!) &/@Select[Divisors[s c], c <= # <= s &]], {c, 1, s}] (* "Eigenray", see link, Feb 15th 2009 *)

Crossrefs

Sequence in context: A149538 A149539 A007231 * A328494 A149540 A149541

Adjacent sequences: A158342 A158343 A158344 * A158346 A158347 A158348

Keyword

nonn

Author

Harmen Wassenaar (towr(AT)ai.rug.nl), Mar 16 2009

Status

approved