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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 December 16 01:32 EST 2019. Contains 330013 sequences. (Running on oeis4.)