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A227962 Triangle of permutations that assign sona-becs (A227960) to their complements. 1
0, 1, 0, 3, 1, 2, 0, 7, 3, 5, 1, 6, 2, 4, 0, 15, 7, 12, 3, 13, 5, 9, 1, 14, 6, 10, 11, 2, 4, 8, 0, 31, 15, 26, 7, 28, 12, 20, 3, 29, 13, 22, 23, 5, 9, 17, 1, 30, 14, 24, 25, 6, 27, 10, 11, 18, 19, 2, 21, 4, 8, 16, 0 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,4

COMMENTS

Subgroups of nimber addition (sona, A190939) have complements (defined using their Walsh spectrum). All sona in the same sona-bec (A227960) have complements in a unique sona-bec, which thus can be called its complement.

The permutation in row n of this triangle assigns complementary sona-becs of size 2^n to each other. (It is thus self inverse.)

Even rows contain fixed points, because some sona-becs with weight 2^(n/2) are their own complements. E.g. in row 4 the fixed points are 3, 5, 10 and 11.

Each row contains the row before as a subsequence.

0 is always complement with A076766(n)-1, so each row ends with 0, and the left column is A076766-1 (not A000225).

Triangle begins:

    k = 0   1   2   3   4   5   6   7   8   9  10  11  12  13  14  15

n

0       0

1       1   0

2       3   1   2   0

3       7   3   5   1   6   2   4   0

4      15   7  12   3  13   5   9   1  14   6  10  11   2   4   8   0

LINKS

Tilman Piesk, Rows 0...7, flattened

Tilman Piesk, Rows 0...7 (the same with emphasis on subsequences)

Tilman Piesk, Complement pairs for n=0...7

Tilman Piesk, Graphic for n=4, complements are symmetric to each other

Tilman Piesk, Subgroups of nimber addition (Wikiversity)

EXAMPLE

a(4;1)=7 and a(4;7)=1, so 1 and 7 are complements for n=4.

a(4;3)=3, so 3 is its own complement for n=4.

CROSSREFS

Sequence in context: A201671 A226590 A261349 * A255615 A056931 A139569

Adjacent sequences:  A227959 A227960 A227961 * A227963 A227964 A227965

KEYWORD

nonn,tabf

AUTHOR

Tilman Piesk, Aug 04 2013

STATUS

approved

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Last modified November 15 01:22 EST 2019. Contains 329142 sequences. (Running on oeis4.)