A091238 Number of nodes in rooted tree with GF2X-Matula number n.

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, 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, 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

Offset: 1

Author

Antti Karttunen, Jan 03 2004

Keywords

• nonn

Comments

Each n occurs A000081(n) times.

Examples

			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):
................................................o...................o
................................................|...................|
............o...............o...o........o......o...............o...o
............|...............|...|........|......|...............|...|
...o........o......o...o....o...o....o...o......o......o.o.o....o...o
...|........|.......\./......\./......\./.......|.......\|/......\./.
x..x........x........x........x........x........x........x........x..
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
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.
		

Links

• A. Karttunen, Scheme-program for computing this sequence.
• Index entries for sequences operating on GF(2)[X]-polynomials

Crossrefs

a(n) = A061775(A091205(n)). a(A091230(n)) = n+1. Cf. A091239-A091241.