A053725 -id:A053725 - cp's OEIS frontend

A053774 Number of n X n binary matrices of order dividing 9 (i.e., number of solutions of X^9=I in GL(n,2)).

1, 3, 57, 1233, 75393, 339089409, 2607120373761, 42451338836860929, 3767776947041641791489, 355742034243147691726340097, 91926159597577085028716636536833, 97320453584330647458564330111836880897, 145554614131872292109665186286397182040866817

Offset: 1

Vladeta Jovovic, Mar 24 2000

nonn

V. Jovovic, The cycle index polynomials of some classical groups, Belgrade, 1995, unpublished.

Kent E. Morrison, Integer Sequences and Matrices Over Finite Fields, Journal of Integer Sequences, Vol. 9 (2006), Article 06.2.1.

Cf. A053722, A053725, A053718.

\\ See A053725 for F(n,q,k).
F(15, 2, 9) \\ Andrew Howroyd, Jul 09 2018

a(12)-(13) from Andrew Howroyd, Jul 09 2018

A053775 Number of n X n binary matrices of order dividing 10 (i.e., number of solutions of X^10=I in GL(n,2)).

Original entry on oeis.org

1, 4, 22, 1660, 673600, 896315680, 1430468698240, 27959577476915200, 2959021586728806707200, 1022333042228611529224192000, 420758775616050043741512977612800

Offset: 1

Vladeta Jovovic, Mar 24 2000

nonn

V. Jovovic, The cycle index polynomials of some classical groups, Belgrade, 1995, unpublished.

Kent E. Morrison, Integer Sequences and Matrices Over Finite Fields, Journal of Integer Sequences, Vol. 9 (2006), Article 06.2.1.

Cf. A053722, A053725, A053718.

A063387 Number of solutions of x^4=1 in general affine group AGL(n,2).

Original entry on oeis.org

2, 16, 512, 45376, 8556032, 4883562496, 8980929708032, 42613515533418496, 486724235988568113152, 16895428758428581359517696, 1832013338159753885910032187392, 514041193283459103260028716172967936

Offset: 1

Vladeta Jovovic, Jul 16 2001

nonn

V. Jovovic, Cycle index of general affine group AGL(n,2)

Cf. A063385-A063393, A062710, A053722, A053725, A053718, A053770-A053777.

A063388 Number of solutions of x^5=1 in general affine group AGL(n,2).

Original entry on oeis.org

1, 1, 1, 21505, 10665985, 3583770625, 1040317415425, 22653952038273025, 2926557495587739009025, 255470267616151345324621825, 19124940736236376955275154817025, 1747866583310404907502405460766490625

Offset: 1

Vladeta Jovovic, Jul 16 2001

nonn

V. Jovovic, Cycle index of general affine group AGL(n,2)

Cf. A063385-A063393, A062710, A053722, A053725, A053718, A053770-A053777.

A316584 Array read by antidiagonals: T(n,k) is the number of elements x in GL(2,Z_n) with x^k == I mod n where I is the identity matrix.

Original entry on oeis.org

1, 1, 1, 1, 4, 1, 1, 3, 14, 1, 1, 4, 9, 28, 1, 1, 1, 20, 9, 32, 1, 1, 6, 1, 64, 21, 56, 1, 1, 1, 30, 1, 184, 27, 58, 1, 1, 4, 1, 60, 25, 80, 171, 176, 1, 1, 3, 32, 1, 72, 1, 100, 33, 110, 1, 1, 4, 9, 64, 1, 180, 1, 640, 297, 128, 1, 1, 1, 14, 9, 224, 1, 846, 1, 164, 63, 134, 1

Offset: 1

Andrew Howroyd, Jul 07 2018

All columns are multiplicative.

Some terms of this sequence may also be computed using a formula given by Kent Morrison (section 1.11 and 2.5 in the reference). See A053725 for a PARI implementation.

			Array begins:
======================================================
  n\k | 1   2   3    4    5    6   7    8   9   10
------+-----------------------------------------------
    1 | 1   1   1    1    1    1   1    1   1    1 ...
    2 | 1   4   3    4    1    6   1    4   3    4 ...
    3 | 1  14   9   20    1   30   1   32   9   14 ...
    4 | 1  28   9   64    1   60   1   64   9   28 ...
    5 | 1  32  21  184   25   72   1  224  21   80 ...
    6 | 1  56  27   80    1  180   1  128  27   56 ...
    7 | 1  58 171  100    1  846  49  184 171   58 ...
    8 | 1 176  33  640    1  432   1 1024  33  176 ...
    9 | 1 110 297  164    1 1566   1  272 729  110 ...
   10 | 1 128  63  736   25  432   1  896  63  320 ...
   11 | 1 134 111  244 1325  354   1  464 111 5950 ...
   12 | 1 392  81 1280    1 1800   1 2048  81  392 ...
   13 | 1 184 549 1096    1 2736 469 1408 549  184 ...
   14 | 1 232 513  400    1 5076  49  736 513  232 ...
   15 | 1 448 189 3680   25 2160   1 7168 189 1120 ...
   ...

Kent E. Morrison, Integer Sequences and Matrices Over Finite Fields, Journal of Integer Sequences, Vol. 9 (2006), Article 06.2.1.

Column 2 is A066907.

Cf. A053725, A316566, A316586.

T(n,k) = Sum_{d|k} A316566(n, d).

Conjecture: T(p,p) = p^2 for p prime.

A053776 Number of n X n binary matrices of order dividing 11 (i.e., number of solutions of X^11=I in GL(n,2)).

Original entry on oeis.org

1, 1, 1, 1, 1, 1, 1, 1, 1, 358201502736997192984166401, 750836199529096452135514747699201, 1049488806253789856936937093744033792001, 1257525074216198249058077510927708275605504001, 1406432139324346089084141831613688810103123424051201

Offset: 1

Vladeta Jovovic, Mar 24 2000

nonn

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

Kent E. Morrison, Integer Sequences and Matrices Over Finite Fields, Journal of Integer Sequences, Vol. 9 (2006), Article 06.2.1.

Cf. A053722, A053725, A053718.

\\ See A053725 for F(n,q,k).
F(15, 2, 11) \\ Andrew Howroyd, Jul 09 2018

A063389 Number of solutions of x^6=1 in general affine group AGL(n,2).

Original entry on oeis.org

2, 18, 540, 75168, 35803296, 52295889024, 165440621998080, 1667054559389773824, 57054517078704967876608, 7229212455140774474869112832, 3089828410800189940613202019614720

Offset: 1

Vladeta Jovovic, Jul 16 2001

nonn

V. Jovovic, Cycle index of general affine group AGL(n,2)

Cf. A063385-A063393, A062710, A053722, A053725, A053718, A053770-A053777.

A063390 Number of solutions of x^7=1 in general affine group AGL(n,2).

Original entry on oeis.org

1, 1, 385, 46081, 3809281, 27335393281, 219971402072065, 1196544590358773761, 34605327838407410319361, 15221801372279275206853263361, 5309386094113063403935896849874945

Offset: 1

Vladeta Jovovic, Jul 16 2001

nonn

V. Jovovic, Cycle index of general affine group AGL(n,2)

Cf. A063385-A063393, A062710, A053722, A053725, A053718, A053770-A053777.

A063391 Number of solutions of x^8=1 in general affine group AGL(n,2).

Original entry on oeis.org

2, 16, 512, 65536, 33554432, 68719476736, 562949953421312, 13098680304497852416, 668820864146264243044352, 107256832111726994824496152576, 61528102027124002571478755339927552

Offset: 1

Vladeta Jovovic, Jul 16 2001

nonn

V. Jovovic, Cycle index of general affine group AGL(n,2)

Cf. A063385-A063393, A062710, A053722, A053725, A053718, A053770-A053777.

A063392 Number of solutions of x^9=1 in general affine group AGL(n,2).

Original entry on oeis.org

1, 9, 225, 6273, 968193, 20785780737, 166595296845825, 8149768955751661569, 951855018651756891865089, 115831656001165053232244326401, 75552701461152667657380793652609025

Offset: 1

Vladeta Jovovic, Jul 16 2001

nonn

V. Jovovic, Cycle index of general affine group AGL(n,2)

Cf. A063385-A063393, A062710, A053722, A053725, A053718, A053770-A053777.

cp's OEIS Frontend

A053774 Number of n X n binary matrices of order dividing 9 (i.e., number of solutions of X^9=I in GL(n,2)).

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A053775 Number of n X n binary matrices of order dividing 10 (i.e., number of solutions of X^10=I in GL(n,2)).

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A063387 Number of solutions of x^4=1 in general affine group AGL(n,2).

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A063388 Number of solutions of x^5=1 in general affine group AGL(n,2).

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A316584 Array read by antidiagonals: T(n,k) is the number of elements x in GL(2,Z_n) with x^k == I mod n where I is the identity matrix.

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A053776 Number of n X n binary matrices of order dividing 11 (i.e., number of solutions of X^11=I in GL(n,2)).

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A063389 Number of solutions of x^6=1 in general affine group AGL(n,2).

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A063390 Number of solutions of x^7=1 in general affine group AGL(n,2).

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A063391 Number of solutions of x^8=1 in general affine group AGL(n,2).

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A063392 Number of solutions of x^9=1 in general affine group AGL(n,2).

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