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A216477
The sequence of the parts in the partition binary diagram represented as an array.
0
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)
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
KEYWORD
nonn
AUTHOR
Mircea Merca, Sep 10 2012
STATUS
approved