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 A228368 Difference between the n-th element of the ruler function and the highest power of 2 dividing n. 2
 0, 0, 0, -1, 0, 0, 0, -4, 0, 0, 0, -1, 0, 0, 0, -11, 0, 0, 0, -1, 0, 0, 0, -4, 0, 0, 0, -1, 0, 0, 0, -26, 0, 0, 0, -1, 0, 0, 0, -4, 0, 0, 0, -1, 0, 0, 0, -11, 0, 0, 0, -1, 0, 0, 0, -4, 0, 0, 0, -1, 0, 0, 0, -57, 0, 0, 0, -1, 0, 0, 0, -4, 0, 0, 0, -1, 0, 0, 0, -11, 0, 0, 0, -1, 0, 0, 0, -4, 0, 0, 0, -1, 0, 0, 0, -26 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,8 COMMENTS Also rank of the n-th region of the diagram of compositions of j, if 1 <= n <= 2^(j-1), see example. Here the rank of a region is defined as the largest part minus the number of parts (similar to the Dyson's rank of a partition). The equivalent sequence for integer partitions is A194447. Also triangle read by rows in which T(j,k) is the rank of the k-th region of the j-th section of the set of compositions in colexicographic order of any integer >= j. See A228366. LINKS Antti Karttunen, Table of n, a(n) for n = 1..65537 FORMULA a(n) = A001511(n) - A006519(n). a(4n-3) = a(4n-2) = a(4n-1) = 0. a(4n) = A001511(4n) - A006519(4n). EXAMPLE Illustration of initial terms (n = 1..16): ----------------------------------------------- .                  Largest     Number of .    Diagram of    part of     parts of .   compositions   region n    region n ----------------------------------------------- n                 A001511(n)  A006519(n)  a(n) ----------------------------------------------- . 1     _| | | | |      1           1         0 2     _ _| | | |      2           2         0 3     _|   | | |      1           1         0 4     _ _ _| | |      3           4        -1 5     _| |   | |      1           1         0 6     _ _|   | |      2           2         0 7     _|     | |      1           1         0 8     _ _ _ _| |      4           8        -4 9     _| | |   |      1           1         0 10    _ _| |   |      2           2         0 11    _|   |   |      1           1         0 12    _ _ _|   |      3           4        -1 13    _| |     |      1           1         0 14    _ _|     |      2           2         0 15    _|       |      1           1         0 16    _ _ _ _ _|      5          16       -11 . Written as an array read by rows with four columns the first three columns contain only zeros.   0,   0,   0,  -1;   0,   0,   0,  -4;   0,   0,   0,  -1;   0,   0,   0, -11;   0,   0,   0,  -1;   0,   0,   0,  -4;   0,   0,   0,  -1;   0,   0,   0, -26;   ... Written as a triangle T(j,k) the sequence begins: 0; 0; 0,-1; 0,0,0,-4; 0,0,0,-1,0,0,0,-11; 0,0,0,-1,0,0,0,-4,0,0,0,-1,0,0,0,-26; 0,0,0,-1,0,0,0,-4,0,0,0,-1,0,0,0,-11,0,0,0,-1,0,0,0,-4,0, 0,0,-1,0,0,0,-57; ... Row lengths give A011782. CROSSREFS Cf. A001511, A006519, A011782, A141285, A194446, A194447, A228366, A228367, A228525. Sequence in context: A005925 A333037 A070206 * A267701 A128975 A245817 Adjacent sequences:  A228365 A228366 A228367 * A228369 A228370 A228371 KEYWORD sign,tabf AUTHOR Omar E. Pol, Aug 22 2013 STATUS approved

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Last modified May 28 17:37 EDT 2020. Contains 334684 sequences. (Running on oeis4.)