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A186081 Number of binary relations R on {1,2,...,n} such that the transitive closure of R is the trivial relation. 0
1, 1, 4, 144, 25696, 18082560, 47025585664 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

LINKS

Table of n, a(n) for n=0..6.

EXAMPLE

a(2)=4 because there are four relations on {1,2} whose transitive closure is {(1,1), (1,2), (2,1), (2,2)}. They are the three nontransitive relations,{(1,2), (2,1)}, {(1,2), (2,1), (2,2)}, {(1,1), (1,2), (2,1)} and the trivial relation itself.

MATHEMATICA

f[list_] := Apply[Plus, Table[MatrixPower[list, n], {n, 1, Length[list]}]]; Table[Length[Select[Map[Flatten, Map[f, Tuples[Strings[{0, 1}, n], n]]], FreeQ[#, 0] &]], {n, 0, 4}]

a[ n_] := If[ n < 1, Boole[n == 0], With[{triv = matnk[n, 2^n^2 - 1]}, Sum[ Boole[triv === transitiveClosure[ matnk[n, k]]], {k, 0, 2^n^2 - 1}]]]; matnk[n_, k_] := Partition[ IntegerDigits[ k, 2, n^2], n]; transitiveClosure[x_] := FixedPoint[ Sign@(# + Dot[#, x]) &, x, Length@x]; (* Michael Somos, Mar 08 2012 *)

CROSSREFS

Cf. A002416.

Sequence in context: A186418 A122747 A069135 * A138176 A203424 A055209

Adjacent sequences:  A186078 A186079 A186080 * A186082 A186083 A186084

KEYWORD

nonn,nice,more

AUTHOR

Geoffrey Critzer, Feb 12 2011

EXTENSIONS

a(0)=1 prepended by Alois P. Heinz, Aug 31 2015

a(6) from Bert Dobbelaere, Feb 16 2019

STATUS

approved

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Last modified April 20 22:22 EDT 2019. Contains 322310 sequences. (Running on oeis4.)