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A126235
Minimum length of a codeword in Huffman encoding of n symbols, where the k-th symbol has frequency k.
3
1, 1, 1, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 6, 6, 6, 6, 6, 6, 6, 6, 6
OFFSET
2,4
LINKS
M. J. Fisher et al., The birank number of a graph, Congressus Numerant., 204 (2010), 173-180.
Wikipedia, Huffman coding
FORMULA
Conjecture: a(n) = A099396(n+1) = floor(log_2(2(n+1)/3)). Equivalently, a(n) = a(n-1) + 1 if n has the form 3*2^k-1, a(n) = a(n-1) 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 shortest codewords have length a(8)=2.
CROSSREFS
Cf. A099396, A126014 and A126237. The maximum length of a codeword is in A126236.
Sequence in context: A081604 A123119 A099396 * A220104 A191228 A340763
KEYWORD
nonn,changed
AUTHOR
Dean Hickerson, Dec 21 2006
STATUS
approved