%I A006167 M2349
%S A006167 1,3,4,8,11,20,27,45,61,95,128,193,257,374,497,703,927,1287,1683,2297,
%T A006167 2987,4013,5186,6887,8843,11614,14836,19294,24514,31622,39968,51167,
%U A006167 64377,81839,102509,129528,161539,202959,252124,315110,389949,485062
%N A006167 Number of factorization patterns of polynomials of degree n over F_2.
%C A006167 Let F_q(n) represent the number of factorization patterns of n with the 
               property that there exists a monic polynomial V of degree n over 
               the finite field F_q such that V factors over F_q into one of the 
               F_q(n) factorization patterns. Sequence is for the q=2 case,
%D A006167 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, 
               Academic Press, 1995 (includes this sequence).
%D A006167 R. A. Hultquist, G. L. Mullen and H. Niederreiter, Association schemes 
               and derived PBIB designs of prime power order, Ars. Combin., 25 (1988), 
               65-82.
%D A006167 A. K. Agarwal and G. L. Mullen, Partitions with "d(a) copies of a", J. 
               Combin. Theory, A48 (1988), 120-135.
%H A006167 T. D. Noe, <a href="b006167.txt">Table of n, a(n) for n=1..1000</a>
%F A006167 Euler transform of sequence b(n) = sum_{d|n, A001037(d)>=n/d} 1. - Frank 
               Adams-Watters (FrankTAW(AT)Netscape.net), Jun 19 2006
%e A006167 For n=3 there are 5 factorization patterns of cubic polynomials: 3, 2 
               + 1, 1^3, 1^2 + 1, 1 + 1 + 1. For example 1^2 + 1 corresponds to 
               a cubic polynomial which factors as a linear of multiplicity 2 and 
               a second distinct linear factor. For q=2 the pattern 1 + 1 + 1 is 
               not allowed since over F_2 there are only two distinct monic irreducibles 
               of degree 1. Thus a(3) = 4.
%Y A006167 Cf. A006168-A006171.
%Y A006167 Cf. A001037.
%Y A006167 Sequence in context: A084421 A024786 A097497 this_sequence A137504 A109794 
               A034417
%Y A006167 Adjacent sequences: A006164 A006165 A006166 this_sequence A006168 A006169 
               A006170
%K A006167 nonn,nice
%O A006167 1,2
%A A006167 N. J. A. Sloane (njas(AT)research.att.com).
%E A006167 Additional comments from Gary Mullen, Jun 03 2003.
%E A006167 More terms from Frank Adams-Watters (FrankTAW(AT)Netscape.net), Jun 19 
               2006