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
A115500
Number of monic irreducible polynomials of degree 1 in GF(2^n)[x1,x2,x3,x4].
Original entry on oeis.org
30, 340, 4680, 69904, 1082400, 17043520, 270549120, 4311810304, 68853957120, 1100586419200, 17600780175360, 281543712968704, 4504149450301440, 72061992352890880, 1152956690052710400, 18447025552981295104, 295150156996346511360, 4722384497336874434560, 75558007841377277706240
Offset: 1
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CoefficientList[Series[(30 - 560 x + 2880 x^2 - 4096 x^3)/((1 - 2 x) (1 - 4 x) (1 - 8 x) (1 - 16 x)), {x, 0, 20}], x] (* Vincenzo Librandi, Apr 28 2014 *)
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a(n) = numirrpol(2^n, 4, 1)[1]; \\ using numirrpol script from Max Alekseyev, Michel Marcus, Apr 28 2014
A115459
Number of monic irreducible polynomials of degree n in GF(2)[x1,x2,x3,x4].
Original entry on oeis.org
1, 30, 32271, 34358732510, 1180591619651753817965, 85070591730234579267502316804666675034, 1645504557321206042154966545369006867672093537164814204114794279
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, 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.
A115460
Number of monic irreducible polynomials of degree n in GF(2)[x1,x2,x3,x4,x5].
Original entry on oeis.org
1, 62, 2095135, 72057593905890750, 85070591730234615861304021242850041053, 7237005577332262213973186563042994235469926762597754302088290406498628562618
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, 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.
A115462
Number of monic irreducible polynomials of degree n in GF(3)[x,y,z].
Original entry on oeis.org
1, 39, 28704, 1742232560, 25015702424562603, 261673815513000717140575872, 5986257591270542940940766674496702426288, 898505149957215365756286256207383540787286531952289973040
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, 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.
A115463
Number of monic irreducible polynomials of degree n in GF(3)[x1,x2,x3,x4].
Original entry on oeis.org
1, 120, 7167072, 25015771681981520, 1251577752496617773723676099629193, 655010254318810176195603896415342984711897764371763012689776
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, 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.
A115464
Number of monic irreducible polynomials of degree n in GF(3)[x1,x2,x3,x4,x5].
Original entry on oeis.org
1, 363, 5230110171, 261673816513678364838549056, 655010254318810176195604047856155787712898209939105520303339
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, 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.
A115466
Number of monic irreducible polynomials of degree n in GF(5)[x,y,z].
Original entry on oeis.org
1, 155, 2429160, 23841478316240, 727595757696091789500850, 346944695195247913885977115917541969344, 12924697071141057365742388361357854155242942276714117373280
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, 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.
A115467
Number of monic irreducible polynomials of degree n in GF(5)[x1,x2,x3,x4].
Original entry on oeis.org
1, 780, 7629089160, 727595761412384191996240, 2117582368135750847670237999380338002646893205850, 2938735877055718769921841343055614192892832062416197386190308265258845498373735129547344
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, 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.