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A006691 Normalized number of connected n-state finite automata with 2 inputs.
(Formerly M4662)
6
9, 148, 3493, 106431, 3950832, 172325014, 8617033285, 485267003023, 30363691715629, 2088698040637242, 156612539215405732, 12709745319947141220, 1109746209390479579732, 103724343230007402591558 (list; graph; refs; listen; history; text; internal format)
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 671-685 in "Graph theory with applications to algorithms and computer science." Proceedings of the fifth international conference held at Western Michigan University, Kalamazoo, Mich., June 4-8, 1984. Edited by Y. Alavi, G. Chartrand, L. Lesniak [L. M. Lesniak-Foster], D. R. Lick and C. E. Wall. A Wiley-Interscience Publication. John Wiley & Sons, Inc., New York, 1985. xv+810 pp. ISBN: 0-471-81635-3; 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 671-685 in "Graph theory with applications to algorithms and computer science." Proceedings of the fifth international conference held at Western Michigan University, Kalamazoo, Mich., June 4-8, 1984. Edited by Y. Alavi, G. Chartrand, L. Lesniak [L. M. Lesniak-Foster], D. R. Lick and C. E. Wall. A Wiley-Interscience Publication. John Wiley & Sons, Inc., New York, 1985. xv+810 pp. ISBN: 0-471-81635-3; 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] (* Jean-Fran├žois 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

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Last modified November 21 22:40 EST 2019. Contains 329383 sequences. (Running on oeis4.)