A000585 -id:A000585 - cp's OEIS frontend

A000214 Number of equivalence classes of Boolean functions of n variables under action of AG(n,2).

Original entry on oeis.org

3, 5, 10, 32, 382, 15768919, 16224999167506438730294, 84575066435667906978109556031081616704183639810103015118

Offset: 1

N. J. A. Sloane

AG denotes affine group.

V. Jovovic, The cycle indices polynomials of some classical groups, Belgrade, 1995, unpublished.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

Kenny Lau, Table of n, a(n) for n = 1..10 (one digit in a(9) corrected by _Georg Fischer_, Apr 13 2019)
H. Fripertinger, Cycle indices of linear, affine and projective groups, Linear Algebra and Its Applications, 263, 133-156, 1997.
H. Fripertinger, Implementation of cycle index of linear group
M. A. Harrison, On the classification of Boolean functions by the general linear and affine groups, Technical Note, (1962).
M. A. Harrison, On the classification of Boolean functions by the general linear and affine groups, J. Soc. Industrial and Applied Mathematics, 12.2 (1964), 285-299. [This journal later became the SIAM Journal]
M. A. Harrison, On asymptotic estimates in switching and automata theory, J. Assoc. Comput. Mach. 13 1966, 151-157.
Vladeta Jovovic, Cycle indices
Index entries for sequences related to Boolean functions

Cf. A000585.

More terms from Vladeta Jovovic

A028407 Number of equivalence classes of Boolean functions of n variables under action of LSD(n,2).

Original entry on oeis.org

4, 12, 44, 344, 33328, 58616531552, 263752837930654539573558624, 5521060336920386409400918079935910963482577804036340308751264

Offset: 1

N. J. A. Sloane

nonn

Linear self-dual group LSD(n,2) is group of n X n non-singular matrices over GF(2) with odd number of units in each row.

V. Jovovic, The cycle index polynomials of some classical groups, Belgrade, 1995, unpublished.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. A000585.

More terms from Vladeta Jovovic

A000613 Number of Boolean functions of n variables.

Original entry on oeis.org

2, 4, 10, 46, 1372, 475499108, 1038397981840994509577948, 10825608503765473087803384381127710579846422820261084889808

Offset: 1

N. J. A. Sloane

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.
Index entries for sequences related to Boolean functions

Cf. A000585.

a(n) = A000585(n)/2. - Sean A. Irvine, Mar 21 2011

More terms from Vladeta Jovovic, Feb 23 2000

A053874 Triangle T(n,k) = number of Boolean functions mapping {0,1}^n to {0,1}^n with image of size k (k = 0...2^n) under action of GL(n,2).

Original entry on oeis.org

1, 2, 1, 1, 2, 2, 2, 1, 1, 2, 2, 3, 4, 3, 2, 2, 1, 1, 2, 2, 3, 5, 7, 9, 11, 12, 11, 9, 7, 5, 3, 2, 2, 1, 1, 2, 2, 3, 5, 8, 14, 23, 35, 55, 84, 117, 158, 204, 242, 274, 290, 274, 242, 204, 158, 117, 84, 55, 35, 23, 14, 8, 5, 3, 2, 2, 1, 1, 2, 2, 3, 5, 8, 15, 29, 54, 107, 227, 495, 1131

Offset: 1

Vladeta Jovovic, Mar 30 2000

			Triangle begins:
  1, 2, 1;
  1, 2, 2, 2, 1;
  1, 2, 2, 3, 4, 3, 2, 2, 1;
  ...

Sean A. Irvine, Java program (github)
Index entries for sequences related to Boolean functions

Row sums give A000585.

A049869 Number of equivalence classes of 3-valued Post functions of n variables under action of group GL(n,3).

Original entry on oeis.org

1, 18, 648, 683253810, 18277247229553861734086286719130, 183338496737597442552032556385320299285077278828958986337475538895489368739369176364504064357258701313760

Offset: 0

Vladeta Jovovic

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

Cf. A000585.

cp's OEIS Frontend

A000214 Number of equivalence classes of Boolean functions of n variables under action of AG(n,2).

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A028407 Number of equivalence classes of Boolean functions of n variables under action of LSD(n,2).

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A000613 Number of Boolean functions of n variables.

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A053874 Triangle T(n,k) = number of Boolean functions mapping {0,1}^n to {0,1}^n with image of size k (k = 0...2^n) under action of GL(n,2).

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A049869 Number of equivalence classes of 3-valued Post functions of n variables under action of group GL(n,3).

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