

A126236


Maximum length of a codeword in Huffman encoding of n symbols, where the kth 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
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OFFSET

2,2


REFERENCES

M. J. Fisher et al., The birank number of a graph, Congressus Numerant., 204 (2010), 173180.


LINKS

Table of n, a(n) for n=2..84.
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(n1)=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: A072073 A320757 A061716 * A198194 A073047 A038567
Adjacent sequences: A126233 A126234 A126235 * A126237 A126238 A126239


KEYWORD

nonn


AUTHOR

Dean Hickerson, Dec 21 2006


STATUS

approved



