A216477 The sequence of the parts in the partition binary diagram represented as an array.

1, 2, 1, 3, 1, 4, 2, 1, 5, 2, 1, 6, 3, 2, 1, 7, 3, 2, 1, 8, 4, 3, 2, 1, 9, 4, 3, 2, 1, 10, 5, 4, 3, 2, 1, 11, 5, 4, 3, 2, 1, 12, 6, 5, 4, 3, 2, 1, 13, 6, 5, 4, 3, 2, 1, 14, 7, 6, 5, 4, 3, 2, 1, 15, 7, 6, 5, 4, 3, 2, 1, 16, 8, 7, 6, 5, 4, 3, 2, 1

Offset

1,2

Comments

n is followed by the sequence floor(n/2), floor(n/2)-1, ..., 1.

References

Mircea Merca, Binary Diagrams for Storing Ascending Compositions, Comp. J., 2012, (DOI 10.1093/comjnl/bxs111)

Links

Table of n, a(n) for n=1..80.

Formula

If n=k^2 or n=k^2+k then a(n) = ceiling(sqrt(4*n))-1, otherwise a(n) = floor((ceiling(sqrt(4*n))^2)/4) - n.

Example

1,
2, 1,
3, 1,
4, 2, 1,
5, 2, 1,
6, 3, 2, 1,
7, 3, 2, 1,
8, 4, 3, 2, 1,
9, 4, 3, 2, 1,
10, 5, 4, 3, 2, 1,
11, 5, 4, 3, 2, 1,
12, 6, 5, 4, 3, 2, 1,
13, 6, 5, 4, 3, 2, 1,
14, 7, 6, 5, 4, 3, 2, 1,
15, 7, 6, 5, 4, 3, 2, 1,
16, 8, 7, 6, 5, 4, 3, 2, 1

Maple

seq(piecewise(floor((1/4)*ceil(sqrt(4*n))^2)-n = 0, ceil(sqrt(4*n))-1, 0 < floor((1/4)*ceil(sqrt(4*n))^2)-n, floor((1/4)*ceil(sqrt(4*n))^2)-n), n=1..50)

Mathematica

Table[{n, Range[Floor[n/2], 1, -1]}, {n, 20}]//Flatten (* Harvey P. Dale, Jul 16 2017 *)

Crossrefs

Sequence in context: A056538 A266742 A120385 * A195836 A347285 A132460

Adjacent sequences: A216474 A216475 A216476 * A216478 A216479 A216480

Keyword

nonn

Author

Mircea Merca, Sep 10 2012

Status

approved