A126014 Triangle read by rows, based on Huffman encoding. See comments.

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

Offset: 1

Author

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

Keywords

• nonn
• tabf

Comments

Row #n pertains to Huffman encoding of n symbols, where the k-th 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.

Examples

			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; ...
		

Links

• Wikipedia, Huffman coding

Crossrefs

The length of the n-th row is in A126237. The minimum and maximum lengths of codewords are in A126235 and A126236.

Extensions

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