A054745 -id:A054745 - cp's OEIS frontend

A225772 Number of 2-element sets of mapping patterns from n points to themselves; the number of 2-element sets of transformations on n points up to conjugation.

0, 4, 67, 1455, 41829, 1540566, 68342769, 3540690574, 209612913688, 13957423185476, 1032436318249157, 83993175608836193, 7453446303042081363, 716451740543945322472, 74159075140708643215135

Offset: 1

James Mitchell, Jul 26 2013

nonn

J. D. Mitchell, Semigroups data (contains links to files containing the 2-element sets of transformations on n points up to conjugation)

Cf. A001372, A224539.

a(n) = A054745(n) - A001372(n). [James Mitchell, Oct 29 2013]

Added more terms, James Mitchell, Oct 29 2013

A230401 Number of nonisomorphic synchronizing binary n-state automata without output under input permutations.

Original entry on oeis.org

1, 4, 51, 1115, 34265, 1318699, 60477844, 3210707626, 193589241468, 13070085476528

Offset: 1

Marek Szykula, Oct 18 2013

An automaton with the state set Q is synchronizing if there exists a word w such that |Qw|=1.

			For n=2 there are 4 such automata:
[0 a 0,0 b 1,1 a 0,1 b 0],
[0 a 0,0 b 0,1 a 0,1 b 0],
[0 a 0,0 b 1,1 a 0,1 b 1], and
[0 a 0,0 b 0,1 a 1,1 b 0].

A. Kisielewicz and M. Szykuła, Generating Small Automata and the Černý Conjecture, in Implementation and Application of Automata, volume 7982 of LNCS, pages 340-348, 2013.

Cf. A054745, A054746, A230326.

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A225772 Number of 2-element sets of mapping patterns from n points to themselves; the number of 2-element sets of transformations on n points up to conjugation.

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A230401 Number of nonisomorphic synchronizing binary n-state automata without output under input permutations.

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