A000214 -id:A000214 - cp's OEIS frontend

A028405 Number of equivalence classes of Boolean functions of n variables under action of M(n,2).

Original entry on oeis.org

3, 6, 16, 76, 2529, 935339497, 2060570964519821009024090, 21566641941095278268628659206747626784474429009806143425562

Offset: 1

N. J. A. Sloane

Group M(n,2) is semi-direct product of LSD(n,2) (cf. A028407) and complementing group C(n,2).

V. Jovovic, The cycle index polynomials of some classical groups, Belgrade, 1995, unpublished.

V. Jovovic, Cycle indices
I. Strazdins, Universal affine classification of Boolean functions, Acta Applic. Math. 46 (1997), 147-167.
Index entries for sequences related to Boolean functions

Cf. A000214, A049461.

More terms from Vladeta Jovovic

A000614 Number of complemented types of Boolean functions of n variables under action of AG(n,2).

Original entry on oeis.org

2, 3, 6, 18, 206, 7888299, 8112499583888855378066, 42287533217833953489054778023401252726576585396037133766

Offset: 1

N. J. A. Sloane

From Philippe Langevin's article: Let m be a positive integer. The space of Boolean functions from GF(2)^m into GF(2) is denoted by RM(k,m). This notation comes from coding theory, where it is the Reed-Muller code of order k in m variables. The affine group AG(2, m) acts on the spaces RM(k,m), and thus on RM(k,m)/RM(s,m) when s <= k. - Jonathan Vos Post, Feb 08 2011

R. J. Lechner, Harmonic Analysis of Switching Functions, in A. Mukhopadhyay, ed., Recent Developments in Switching Theory, Ac. Press, 1971, pp. 121-254, esp. p. 186.
N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

M. A. Harrison, The number of equivalence classes of Boolean functions under groups containing negation, IEEE Trans. Electron. Comput. 12 (1963), 559-561.
M. A. Harrison, The number of equivalence classes of Boolean functions under groups containing negation, IEEE Trans. Electron. Comput. 12 (1963), 559-561. [Annotated scanned copy]
M. A. Harrison, On the classification of Boolean functions by the general linear and affine groups, J. Soc. Indust. Appl. Math. 12 (1964) 285-299.
Philippe Langevin, Classification of Boolean functions under the affine group, Oct 31, 2009.
Index entries for sequences related to Boolean functions

Cf. A000214.

More terms and better description from Vladeta Jovovic, Feb 24 2000

A053037 Number of self-complementary types of Boolean functions of n variables under action of AG(n,2).

Original entry on oeis.org

1, 1, 2, 4, 30, 7679, 271272025838, 15720888748969530981971252414, 14069509983003731045582973059193483755803287927789561328867085226, 1263863542103738914337052461143370675118811161046459223145205641421535664947642082708619717652803582292264797662579828105738049380777191460

Offset: 1

Vladeta Jovovic, Feb 24 2000

Heuristically a(n) = A000214(n)-A049461(n+1). - R. J. Mathar, Apr 23 2007

V. Jovovic, The cycle index polynomials of some classical groups, Belgrade, 1995, unpublished.

M. A. Harrison, On the classification of Boolean functions by the general linear and affine groups, J. Soc. Indust. Appl. Math. 12 (1964) 285-299.
I. Strazdins, Universal affine classification of Boolean functions, Acta Applic. Math. 46 (1997), 147-167.
Index entries for sequences related to Boolean functions

Cf. A000214, A000614.

A098744 Triangle read by rows: row n gives the number of orbits of the group GA(n) acting on binary vectors of length 2^n and weight k, for n >= 0, 0 <= k <= 2^n.

Original entry on oeis.org

1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 3, 3, 4, 3, 3, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 4, 5, 8, 9, 15, 16, 23, 24, 30, 30, 38, 30, 30, 24, 23, 16, 15, 9, 8, 5, 4, 2, 2, 1, 1, 1, 1

Offset: 0

Alexander Vardy (avardy(AT)ucsd.edu), Nov 15 2008

GA(n) is the general affine group, the automorphism group of the Reed-Muller code RM(r,n).

Since the group is triply transitive, there's only one orbit for vectors of weight 0,1,2,3.

			Triangle begins:
1 1
1 1 1
1 1 1 1 1
1 1 1 1 2 1 1 1 1 (the 2 is because there are two orbits on vectors of length 8 and weight 4)
1 1 1 1 2 2 3 3 4 3 3 2 2 1 1 1 1

Cf. A000214 (row sums). - Vladeta Jovovic, Feb 22 2009

More terms from Vladeta Jovovic, Feb 22 2009

A176637 Partial sums of A000614.

Original entry on oeis.org

2, 5, 11, 29, 235, 7888534, 8112499583888863266600, 42287533217833953489054778023401260839076169284900400366

Offset: 1

Jonathan Vos Post, Apr 22 2010

nonn

Partial sums of complemented types of Boolean functions of n variables under action of AG(n,2). The only known primes in this sequence are the first 4 values: 2, 5, 11, 29.

			a(5) = 2 + 3 + 6 + 18 + 206 = 235.

Cf. A000214, A000614.

a(n) = SUM[i=1..n] A000614(i).

cp's OEIS Frontend

A028405 Number of equivalence classes of Boolean functions of n variables under action of M(n,2).

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A000614 Number of complemented types of Boolean functions of n variables under action of AG(n,2).

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A053037 Number of self-complementary types of Boolean functions of n variables under action of AG(n,2).

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A098744 Triangle read by rows: row n gives the number of orbits of the group GA(n) acting on binary vectors of length 2^n and weight k, for n >= 0, 0 <= k <= 2^n.

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A176637 Partial sums of A000614.

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