

A126014


Triangle read by rows, based on Huffman encoding. See comments.


6



2, 3, 2, 2, 3, 2, 5, 2, 6, 3, 2, 8, 3, 2, 9, 5, 2, 5, 2, 6, 3, 2, 8, 3, 2, 9, 5, 2, 11, 5, 2, 12, 6, 3, 2, 14, 6, 3, 2, 15, 8, 3, 2, 17, 8, 3, 2, 18, 9, 5, 2, 20, 9, 5, 2, 21, 11, 5, 2, 11, 5, 2, 12, 6, 3, 2, 14, 6, 3, 2, 15, 8, 3, 2, 17, 8, 3, 2, 18, 9, 5, 2, 20, 9, 5, 2, 21, 11, 5, 2
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OFFSET

1,1


COMMENTS

Row #n pertains to Huffman encoding of n symbols, where the kth symbol has frequency k. Let b(k) be the number of bits used to encode the symbol of frequency k. The row has the values of k such that b(k)>b(k+1).
Each row is ordered descendingly; each ends with '2'. Row #3 is first.


LINKS

Table of n, a(n) for n=1..90.
Wikipedia, Huffman coding


EXAMPLE

In row #8, the frequencies are 1,2,3,4,5,6,7,8 and a Huffman encoding is (1>00000, 2>00001, 3>0001, 4>001, 5>010, 6>011, 7>10, 8>11). The codes shrink after k=6,3,2; so row #8 has 6,3,2.
2; 3,2; 2; 3,2; 5,2; 6,3,2; 8,3,2; 9,5,2; 5,2; 6,3,2; 8,3,2; ...


CROSSREFS

The length of the nth row is in A126237. The minimum and maximum lengths of codewords are in A126235 and A126236.
Sequence in context: A329362 A241604 A282900 * A317420 A256795 A273404
Adjacent sequences: A126011 A126012 A126013 * A126015 A126016 A126017


KEYWORD

nonn,tabf


AUTHOR

Serhat Sevki Dincer (mesti_mudam(AT)yahoo.com), Dec 14 2006


EXTENSIONS

Edited by Don Reble, Dec 17 2006 and Dean Hickerson, Dec 21 2006


STATUS

approved



