A115457
Number of monic irreducible polynomials of degree n in GF(2)[x,y].
Original entry on oeis.org
1, 6, 35, 694, 26089, 1862994, 253247715, 66799608630, 34698378752226, 35781375988234520, 73534241823793715433, 301714422751259316744750, 2473763407036784492590791565, 40547483778956508623734286010210
Offset: 0
- Max Alekseyev, Formula for the number of monic irreducible polynomials in a finite field
- Max Alekseyev, PARI scripts for various problems
- Arnaud Bodin, Number of irreducible polynomials in several variables over finite fields, Amer. Math. Monthly, 115 (2008), 653-660.
- J. von zur Gathen, K. Ziegler, Survey on counting special types of polynomials, arXiv preprint arXiv:1407.2970, 2014
- Konstantin Ziegler, Counting Classes of Special Polynomials, Doctoral Dissertation, University of Bonn, June 2014.
A115490
Number of monic irreducible polynomials of degree 4 in GF(2^n)[x].
Original entry on oeis.org
3, 60, 1008, 16320, 261888, 4193280, 67104768, 1073725440, 17179803648, 274877644800, 4398045462528, 70368739983360, 1125899890065408, 18014398442373120, 288230375883276288, 4611686017353646080, 73786976290543239168, 1180591620700231434240, 18889465931409861378048
Offset: 1
A115478
Number of monic irreducible polynomials of degree 3 in GF(3)[x1,...,xn].
Original entry on oeis.org
8, 25520, 1742232560, 25015771681981520, 261673816513678364838549056, 5986257591281009894301357511191882167288, 898505149957215605206589914754802519619582611893609512640
Offset: 1
A115489
Number of monic irreducible polynomials of degree 3 in GF(2^n)[x].
Original entry on oeis.org
2, 20, 168, 1360, 10912, 87360, 699008, 5592320, 44739072, 357913600, 2863310848, 22906490880, 183251935232, 1466015498240, 11728124018688, 93824992215040, 750599937851392, 6004799503073280, 48038396025110528
Offset: 1
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[-(1/3)*2^n+(1/3)*8^n: n in [1..20]]; // Vincenzo Librandi, Jul 25 2014
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LinearRecurrence[{10,-16},{2,20},30] (* Harvey P. Dale, Sep 25 2013 *)
CoefficientList[Series[2/((8 x - 1) (2 x - 1)), {x, 0, 30}], x] (* Vincenzo Librandi, Jul 25 2014 *)
A115504
Number of monic irreducible polynomials of degree 1 in GF(2^n)[x1,x2,x3,x4,x5].
Original entry on oeis.org
62, 1364, 37448, 1118480, 34636832, 1090785344, 34630287488, 1103823438080, 35253226045952, 1127000493261824, 36046397799139328, 1153203048319815680, 36897992296869404672, 1180663682709764194304
Offset: 1
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[2^n+4^n+8^n+16^n+32^n: n in [1..20]]; // Vincenzo Librandi, Jul 25 2014
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CoefficientList[Series[-2 (31 - 1240 x + 14880 x^2 - 63488 x^3 + 81920 x^4)/((4 x - 1) (2 x - 1) (8 x - 1) (16 x - 1) (32 x - 1)), {x, 0, 30}], x] (* Vincenzo Librandi, Jul 25 2014 *)
LinearRecurrence[{62,-1240,9920,-31744,32768},{62,1364,37448,1118480,34636832},20] (* Harvey P. Dale, Oct 07 2019 *)
A115458
Number of monic irreducible polynomials of degree n in GF(2)[x,y,z].
Original entry on oeis.org
1, 14, 903, 1034350, 34343703541, 72057077817486762, 19342812032942216095260047, 1329227995494773618659262698956301950, 46768052394568954962565705269783921192917309706498
Offset: 0
A115461
Number of monic irreducible polynomials of degree n in GF(3)[x,y].
Original entry on oeis.org
1, 12, 273, 25520, 6778629, 5132148528, 11368775698280, 74897449398451680, 1476178370884382958936, 87205387550224830516286800, 15450442981642705273095610563240, 8211400746584626963688710296061894800
Offset: 0
A115465
Number of monic irreducible polynomials of degree n in GF(5)[x,y].
Original entry on oeis.org
1, 30, 3410, 2330240, 7549603600, 118965950703744, 9309505329218297280, 3637689729211851543816960, 7105314552536912564123328420000, 69388718760088702173445263653542192000
Offset: 0
- Max Alekseyev, Formula for the number of monic irreducible polynomials in a finite field
- Max Alekseyev, PARI scripts for various problems
- J. von zur Gathen and K. Ziegler, Survey on counting special types of polynomials, arXiv preprint arXiv:1407.2970 [math.AC], 2014.
- Xiang-dong Hou and Gary L. Mullen, Number of Irreducible Polynomials and Pairs of Relatively Prime Polynomials in Several Variables over Finite Fields, arXiv:0811.3986 [math.NT], 2008.
- Konstantin Ziegler, Counting Classes of Special Polynomials, Doctoral Dissertation, University of Bonn, June 2014.
A115491
Number of monic irreducible polynomials of degree 5 in GF(2^n)[x].
Original entry on oeis.org
6, 204, 6552, 209712, 6710880, 214748352, 6871947648, 219902325504, 7036874417664, 225179981368320, 7205759403792384, 230584300921368576, 7378697629483819008, 236118324143482257408, 7555786372591432335360
Offset: 1
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[(32^(n+1)-16*2^(n+1))/160: n in [1..20]]; // Vincenzo Librandi, Jul 25 2014
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CoefficientList[Series[6/((32 x - 1) (2 x - 1)), {x, 0, 30}], x] (* Vincenzo Librandi, Jul 25 2014 *)
A115492
Number of monic irreducible polynomials of degree 2 in GF(2^n)[x,y].
Original entry on oeis.org
35, 1134, 34748, 1081080, 34077680, 1082126304, 34493939648, 1101659045760, 35218731564800, 1126449661607424, 36037593107790848, 1153062242078423040, 36895739947165675520, 1180627649514161823744, 37779508323708391374848, 1208935042986661734481920
Offset: 1
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CoefficientList[Series[7 (256 x^2 - 108 x + 5)/((2 x - 1) (4 x - 1) (16 x - 1) (32 x - 1)), {x, 0, 40}], x] (* Vincenzo Librandi, Jul 26 2014 *)
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Vec(7*x*(256*x^2-108*x+5)/((2*x-1)*(4*x-1)*(16*x-1)*(32*x-1)) + O(x^100)) \\ Colin Barker, Jul 25 2014
Showing 1-10 of 48 results.