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A003181 Number of P-equivalence classes of nondegenerate Boolean functions of n variables.
(Formerly M0378)
12
2, 2, 8, 68, 3904, 37329264, 25626412300941056, 67516342973185974302549277749387264, 2871827610052485009904013737758920847602293486924450772201235462734479360 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,1

COMMENTS

Also the number of non-isomorphic sets of subsets of {1..n} with union {1..n}. - Gus Wiseman, Aug 05 2019

REFERENCES

S. Muroga, Threshold Logic and Its Applications. Wiley, NY, 1971, p. 38 and 214.

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

LINKS

Alois P. Heinz, Table of n, a(n) for n = 0..12

S. Muroga, Threshold Logic and Its Applications, Wiley, NY, 1971 [Annotated scans of a few pages]

Index entries for sequences related to Boolean functions

FORMULA

a(n) = A003180(n)-A003180(n-1), for n>=1. - Christian Sievers, Jul 22 2016

a(n) = 2 * A055621(n). - Gus Wiseman, Aug 05 2019

EXAMPLE

From Gus Wiseman, Aug 05 2019: (Start)

Non-isomorphic representatives of the a(0) = 2 through a(2) = 8 sets of subsets:

  {}    {{1}}     {{1,2}}

  {{}}  {{},{1}}  {{1},{2}}

                  {{},{1,2}}

                  {{2},{1,2}}

                  {{},{1},{2}}

                  {{},{2},{1,2}}

                  {{1},{2},{1,2}}

                  {{},{1},{2},{1,2}}

(End)

MAPLE

b:= proc(n, i, l) `if`(n=0, 2^(w-> add(mul(2^igcd(t, l[h]),

      h=1..nops(l)), t=1..w)/w)(ilcm(l[])), `if`(i<1, 0,

      add(b(n-i*j, i-1, [l[], i$j])/j!/i^j, j=0..n/i)))

    end:

a:= n-> `if`(n=0, 2, b(n$2, [])-b(n-1$2, [])):

seq(a(n), n=0..8);  # Alois P. Heinz, Aug 14 2019

CROSSREFS

Cf. A000371, A001146, A003180, A003465, A055621, A007537, A326881.

Sequence in context: A053978 A181264 A224766 * A009616 A005615 A048617

Adjacent sequences:  A003178 A003179 A003180 * A003182 A003183 A003184

KEYWORD

nonn

AUTHOR

N. J. A. Sloane.

EXTENSIONS

More terms from Christian Sievers, Jul 22 2016

Definition clarified by Ivo Timoteo, Mar 14 2017

STATUS

approved

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Last modified April 5 06:13 EDT 2020. Contains 333238 sequences. (Running on oeis4.)