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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.)