

A006691


Normalized number of connected nstate finite automata with 2 inputs.
(Formerly M4662)


6



9, 148, 3493, 106431, 3950832, 172325014, 8617033285, 485267003023, 30363691715629, 2088698040637242, 156612539215405732, 12709745319947141220, 1109746209390479579732, 103724343230007402591558
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OFFSET

1,1


COMMENTS

Is this sequence essentially the same as A304312?  Paul D. Hanna, May 11 2018


REFERENCES

Robert W. Robinson, Counting strongly connected finite automata, pages 671685 in "Graph theory with applications to algorithms and computer science." Proceedings of the fifth international conference held at Western Michigan University, Kalamazoo, Mich., June 48, 1984. Edited by Y. Alavi, G. Chartrand, L. Lesniak [L. M. LesniakFoster], D. R. Lick and C. E. Wall. A WileyInterscience Publication. John Wiley & Sons, Inc., New York, 1985. xv+810 pp. ISBN: 0471816353; Math Review MR0812651 (86g:05026).
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).


LINKS

Hugo Pfoertner, Table of n, a(n) for n = 1..28
R. W. Robinson, Counting strongly connected finite automata, pages 671685 in "Graph theory with applications to algorithms and computer science." Proceedings of the fifth international conference held at Western Michigan University, Kalamazoo, Mich., June 48, 1984. Edited by Y. Alavi, G. Chartrand, L. Lesniak [L. M. LesniakFoster], D. R. Lick and C. E. Wall. A WileyInterscience Publication. John Wiley & Sons, Inc., New York, 1985. xv+810 pp. ISBN: 0471816353; Math Review MR0812651. (86g:05026). [Annotated scanned copy, with permission of the author.]


FORMULA

a(n) = A027834(n+1)/n!.  Valery A. Liskovets, May 21 2018


MATHEMATICA

v[r_, n_] := v[r, n] = If[n == 0, 1, n^(r*n)  Sum[Binomial[n, t] * n^(r*(n  t)) * v[r, t] , {t, 1, n  1}]];
s[r_, n_] := s[r, n] = v[r, n] + Sum[Binomial[n  1, t  1] * v[r, n  t] * s[r, t], {t, 1, n  1}]
A027834[n_] := s[2, n];
a[n_] := A027834[n + 1]/n!;
Array[a, 28] (* JeanFrançois Alcover, Aug 27 2019 *)


CROSSREFS

Cf. A027834, A304312.
Sequence in context: A241797 A222439 A211106 * A304312 A050580 A266128
Adjacent sequences: A006688 A006689 A006690 * A006692 A006693 A006694


KEYWORD

nonn


AUTHOR

N. J. A. Sloane.


EXTENSIONS

Extended using the formula by Valery A. Liskovets by Hugo Pfoertner, May 21 2018


STATUS

approved



