

A269752


Table of inverse permutations of the rows of A131987: Position of numbers inserted in "storage order" into a perfect binary table of 2^k1 nodes.


1



1, 2, 1, 3, 4, 2, 6, 1, 3, 5, 7, 8, 4, 12, 2, 6, 10, 14, 1, 3, 5, 7, 9, 11, 13, 15, 16, 8, 24, 4, 12, 20, 28, 2, 6, 10, 14, 18, 22, 26, 30, 1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29, 31, 32, 16, 48, 8, 24, 40, 56, 4, 12, 20, 28, 36, 44, 52, 60, 2
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OFFSET

1,2


COMMENTS

Row n is the permutation of {1,...,2^n1} which is the inverse of row n of A131987. See example for an illustration.


LINKS



EXAMPLE

Row 4 of A131987 is obtained by reading the following binary tree, filled with numbers {1,...,15} in "storage order", from the leftmost to the rightmost number:
_____1_____
__2__ __3__
4 5 6 7
8 9 10 11 12 13 14 15
This yields the sequence p = (8, 4, 9, 2, 10, 5, 11, 1, 12, 6, 13, 3, 14, 7, 15) which is a permutation of (1, ..., 15). Row 4 of the present table yields the inverse permutation p' = (8, 4, 12, 2, 6, 10, 14, 1, 3, 5, 7, 9, 11, 13, 15), where p'(i) is the index of i in p, e.g. p'(3)=12 because 3 = p(12).


PROG



CROSSREFS



KEYWORD

nonn,tabf


AUTHOR



STATUS

approved



