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Search: id:A106456
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| A106456 |
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Natural numbers mapped to Dyck path encodings of the rooted plane trees obtained by recursing on the exponents of the GF(2)[X] factorization of n. |
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+0
10
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| 0, 10, 1010, 1100, 110010, 101100, 101010, 110100, 10110010, 11001100, 10101010, 10110100, 1010101010, 10101100, 11010010, 111000, 11100010, 1011001100, 101010101010, 1100110100, 11001010, 1010101100, 101010110010
(list; graph; listen)
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OFFSET
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1,2
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COMMENT
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Note that we recurse on the exponent + 1 for all other irreducible polynomials except the largest one in the GF(2)[X] factorization. Thus for 6 = A048723(3,1) X A048723(2,1) we construct a tree by joining trees 1 and 2 with a new root node, for 7 = A048723(7,1) X A048723(3,0) X A048723(2,0) we join three 1-trees (single leaves) with a new root node, for 8 = A048273(2,3) we add a single edge below tree 3 and for 9 = A048723(7,1) X A048723(3,1) X A048273(2,0) we connect the trees 1 and 2 and 1 with a new root node.
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LINKS
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A. Karttunen, Scheme-program for computing this sequence.
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EXAMPLE
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The rooted plane trees encoded here are:
.....................o....o..........o.........o...o....o.....
.....................|....|..........|..........\./.....|.....
.......o....o...o....o....o...o..o...o..o.o.o....o....o.o.o...
.......|.....\./.....|.....\./....\./....\|/.....|.....\|/....
*......*......*......*......*......*......*......*......*.....
1......2......3......4......5......6......7......8......9.....
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CROSSREFS
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a(n) = A007088(A106455(n)) = A075166(A106443(n)). GF(2)[X]-analogue of A075166. Permutation of A063171. Same sequence shown in decimal: A106455. The digital length of each term / 2 (the number of o-nodes in the corresponding trees) is given by A106457. Cf. A106451-A106454.
Sequence in context: A075166 A071671 A075171 this_sequence A079214 A163662 A080070
Adjacent sequences: A106453 A106454 A106455 this_sequence A106457 A106458 A106459
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KEYWORD
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nonn
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AUTHOR
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Antti Karttunen (His-Firstname.His-Surname(AT)iki.fi), May 09 2005
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