A062710
Number of cyclic subgroups of general affine group over GF(2), AGL(n,2).
Original entry on oeis.org
2, 17, 590, 105824, 69300688, 194965719104, 2426497181267968, 177803451495373322240, 52976870608237776911450112, 110350007913361454793759188320256
Offset: 1
a(3) = 1/phi(1)+91/phi(2)+224/phi(3)+420/phi(4)+224/phi(6)+384/phi(7) = 590.
- V. Jovovic, The cycle index polynomials of some classical groups, Belgrade, 1995, unpublished.
A063393
Number of solutions of x^10=1 in general affine group AGL(n,2).
Original entry on oeis.org
2, 10, 92, 23200, 21391520, 35841831040, 95709758320640, 6206883395497062400, 1502803598296957497344000, 654083813715060854940290252800, 450433384822340709737677746549555200
Offset: 1
A063385
Number of solutions of x^2=1 in general affine group AGL(n,2).
Original entry on oeis.org
2, 10, 92, 1696, 59552, 4124800, 556101632, 148425895936, 78099471368192, 81705857229783040, 169694608681978560512, 702657511446831375056896, 5797142351555426979908943872, 95500953266115919784543392890880, 3140561514292519005433439594146168832
Offset: 1
A063406
Number of cyclic subgroups of order 3 of general affine group AGL(n,2).
Original entry on oeis.org
0, 4, 112, 3136, 484096, 153545728, 72255188992, 169225143107584, 767806696376172544, 5846826552577416232960, 211692077904149369184059392, 14577670180222125357773973618688
Offset: 1
A063413
Number of cyclic subgroups of order 10 of general affine group AGL(n,2).
Original entry on oeis.org
0, 0, 0, 0, 2666496, 8063483904, 23667221200896, 1546057323758223360, 374969260180817571741696, 163457085861840749434433961984, 112603564970401075916528447354044416, 152237556325944043707910988547266571141120, 824860715471760736216894023298196038268145893376
Offset: 1
A053651
Number of nonisomorphic cyclic subgroups of general linear group GL(n,2).
Original entry on oeis.org
1, 3, 5, 8, 13, 18, 27, 37, 51, 70, 96, 130, 176, 232, 296, 380, 490, 620, 793, 1019, 1277, 1624
Offset: 1
a(5)=13 because the orders of the elements of GL(5,2) are {1,2,3,4,5,6,7,8,12,14,15,21,31}.
- V. Jovovic, The cycle index polynomials of some classical groups, Belgrade, 1995, unpublished.
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
- V. Jovovic, The cycle indices polynomials of some classical groups, Belgrade, 1995, unpublished.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
A000585
Number of equivalence classes of Boolean functions of n variables under GL(n,2).
Original entry on oeis.org
4, 8, 20, 92, 2744, 950998216, 2076795963681989019155896, 21651217007530946175606768762255421159692845640522169779616
Offset: 1
- 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).
- 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 asymptotic estimates in switching and automata theory, J. ACM, v. 13, no. 1, Jan. 1966, pp. 151-157.
- Vladeta Jovovic, Cycle indices
- Index entries for sequences related to Boolean functions
A062250
Number of cyclic subgroups of Chevalley group A_n(2) (the group of nonsingular n X n matrices over GF(2) ).
Original entry on oeis.org
1, 5, 79, 6974, 2037136, 2890467344, 14011554132032, 325330342132674560, 27173394819858612320256, 10158190320726534408118452224, 13156630408268153048253765001412608, 80280189722884518774834501142737770774528
Offset: 1
Ahmed Fares (ahmedfares(AT)my-deja.com), Jul 01 2001
a(3) = 1/phi(1)+21/phi(2)+56/phi(3)+42/phi(4)+48/phi(7) = 79.
- V. Jovovic, The cycle index polynomials of some classical groups, Belgrade, 1995, unpublished.
A063386
Number of solutions of x^3=1 in general affine group AGL(n,2).
Original entry on oeis.org
1, 9, 225, 6273, 968193, 307091457, 144510377985, 338450286215169, 1535613392752345089, 11693653105154832465921, 423384155808298738368118785, 29155340360444250715547947237377
Offset: 1
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