A106456 - OEIS

A106456

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.

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; refs; listen; history; text; internal format)

OFFSET

1,2

COMMENTS

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.

LINKS

Table of n, a(n) for n=1..23.

A. Karttunen, Scheme-program for computing this sequence.

EXAMPLE

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.....

CROSSREFS

a(n) = A007088(A106455(n)) = A075166(A106443(n)). GF(2)[X]-analog 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 * A079214 A377192 A163662

Adjacent sequences: A106453 A106454 A106455 * A106457 A106458 A106459

KEYWORD

nonn,base

AUTHOR

Antti Karttunen, May 09 2005

STATUS

approved