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
A053772
Number of n X n binary matrices of order dividing 7 (i.e., number of solutions of X^7=I in GL(n,2)).
Original entry on oeis.org
1, 1, 49, 5761, 476161, 457113601, 3439085027329, 18696142934507521, 144017748317668638721, 30063679011292374997401601, 10371304522603231166854078660609, 3639433320096084212920229480292679681, 18767347744724322162378748108305552459694081
Offset: 1
- V. Jovovic, The cycle index polynomials of some classical groups, Belgrade, 1995, unpublished.
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)).
Original entry on oeis.org
1, 3, 57, 1233, 75393, 339089409, 2607120373761, 42451338836860929, 3767776947041641791489, 355742034243147691726340097, 91926159597577085028716636536833, 97320453584330647458564330111836880897, 145554614131872292109665186286397182040866817
Offset: 1
- V. Jovovic, The cycle index polynomials of some classical groups, Belgrade, 1995, unpublished.
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
- V. Jovovic, The cycle index polynomials of some classical groups, Belgrade, 1995, unpublished.
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
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
A063505
Number of n X n upper triangular binary matrices over GF(2) B such that B^2 = 0.
Original entry on oeis.org
2, 8, 32, 320, 2592, 57472, 946176, 44302336, 1482686464, 143210315776, 9732400087040, 1915349322694656, 263918421714927616, 105091512697853313024, 29316605112733216538624, 23522116026027393322844160, 13266245323073952003913678848, 21392237922664971275489914126336, 24362629720999005014327927695736832
Offset: 2
Ahmed Fares (ahmedfares(AT)my-deja.com), Jul 30 2001
-
feven:= n -> add((binomial(2*n,n-3*j) - binomial(2*n,n-3*j-1))*2^(n^2-3*j^2-j),j=0..n/3):
fodd:= n -> add((binomial(2*n+1,n-3*j)-binomial(2*n+1,n-3*j-1))*2^(n^2+n-3*j^2-2*j),j=0..n/3):
seq(op([feven(i),fodd(i)]),i=1..20); # Robert Israel, Mar 01 2017
-
a[n_] := Sum[If[EvenQ[n], (Binomial[n, n/2 - 3j] - Binomial[n, n/2 - 3j - 1])*2^((n/2)^2 - 3j^2 - j), (Binomial[n, (n-1)/2 - 3j] - Binomial[n, (n-1)/2 - 3j - 1])*2^(((n-1)/2)^2 + (n-1)/2 - 3j^2 - 2j)], {j, 0, n/3}];
Table[a[n], {n, 2, 20}] (* Jean-François Alcover, Sep 18 2018 *)
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
- V. Jovovic, The cycle index polynomials of some classical groups, Belgrade, 1995, unpublished.
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
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
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