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A091238
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Number of nodes in rooted tree with GF2X-Matula number n.
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6
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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
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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COMMENTS
| Each n occurs A000081(n) times.
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LINKS
| A. Karttunen, Scheme-program for computing this sequence.
Index entries for sequences operating on GF(2)[X]-polynomials
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EXAMPLE
| 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
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............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.
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CROSSREFS
| a(n) = A061775(A091205(n)). a(A091230(n)) = n+1. Cf. A091239-A091241.
Sequence in context: A138663 A056149 A167494 * A178047 A122954 A126571
Adjacent sequences: A091235 A091236 A091237 * A091239 A091240 A091241
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KEYWORD
| nonn
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AUTHOR
| Antti Karttunen (His-Firstname.His-Surname(AT)iki.fi), Jan 03 2004
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