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%I #8 Mar 31 2012 14:02:20
%S 1,2,3,3,5,4,4,4,6,6,4,5,6,5,7,5,9,7,5,7,7,5,8,6,5,7,8,6,6,8,5,6,7,10,
%T 9,8,7,6,8,8,7,8,7,6,10,9,5,7,7,6,11,8,7,9,6,7,10,7,7,9,6,6,9,7,11,8,
%U 8,11,7,10,8,9,6,8,12,7,9,9,8,9,11,8,9,9,13,8,10,7,8,11,8,10,8,6,9,8
%N Number of nodes in rooted tree with GF2X-Matula number n.
%C Each n occurs A000081(n) times.
%H A. Karttunen, <a href="/A091247/a091247.scm.txt">Scheme-program for computing this sequence.</a>
%H <a href="/index/Ge#GF2X">Index entries for sequences operating on GF(2)[X]-polynomials</a>
%e GF2X-Matula numbers for unoriented rooted trees are constructed otherwise just like the standard Matula-Goebel numbers (cf. A061773), but instead of normal factorization in N, one factorizes in polynomial ring GF(2)[X] as follows. Here IR(n) is the n-th irreducible polynomial (A014580(n)) and X stands for GF(2)[X]-multiplication (A048720):
%e ................................................o...................o
%e ................................................|...................|
%e ............o...............o...o........o......o...............o...o
%e ............|...............|...|........|......|...............|...|
%e ...o........o......o...o....o...o....o...o......o......o.o.o....o...o
%e ...|........|.......\./......\./......\./.......|.......\|/......\./.
%e x..x........x........x........x........x........x........x........x..
%e 1..2 = IR(1)..3 = IR(2)..4 = 2 X 2....5 = 3 X 3....6 = 2 X 3....7 = IR(3)..8 = 2 X 2 X 2..9 = 3 X 7
%e Counting the vertices (marked with x's and o's) of each tree above, we get the eight initial terms of this sequence: 1,2,3,3,5,4,4,4,6.
%Y a(n) = A061775(A091205(n)). a(A091230(n)) = n+1. Cf. A091239-A091241.
%K nonn
%O 1,2
%A _Antti Karttunen_, Jan 03 2004
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