|
| |
|
|
A126236
|
|
Maximum length of a codeword in Huffman encoding of n symbols, where the k-th symbol has frequency k.
|
|
3
| |
|
|
1, 2, 3, 3, 4, 4, 5, 5, 5, 5, 6, 6, 6, 6, 7, 7, 7, 7, 7, 7, 7, 7, 8, 8, 8, 8, 8, 8, 8, 8, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11
(list; graph; refs; listen; history; internal format)
|
|
|
|
OFFSET
| 2,2
|
|
|
REFERENCES
| M. J. Fisher et al., The birank number of a graph, Congressus Numerant., 204 (2010), 173-180.
|
|
|
LINKS
| Wikipedia, Article on Huffman coding
|
|
|
FORMULA
| Conjecture: a(n) = floor(log2(n)) + floor(log2(2n/3)) where 'log2' means the logarithm to the base 2. Equivalently, a(n)-a(n-1)=1 if n has the form 2^k or 3*2^k and =0 otherwise. This is true at least for n up to 1000.
|
|
|
EXAMPLE
| A Huffman code for n=8 is (1->00000, 2->00001, 3->0001, 4->001, 5->010, 6->011, 7->10, 8->11). The longest codewords have length a(8)=5.
|
|
|
CROSSREFS
| Cf. A126014 and A126237. The minimum length of a codeword is in A126235.
Sequence in context: A130500 A072073 A061716 * A073047 A038567 A185195
Adjacent sequences: A126233 A126234 A126235 * A126237 A126238 A126239
|
|
|
KEYWORD
| nonn
|
|
|
AUTHOR
| Dean Hickerson (dean.hickerson(AT)yahoo.com), Dec 21 2006
|
| |
|
|
