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Search: id:A106624
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| A106624 |
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Cumulative column frequency of occurrence of 0's and 1's iterated in a binary tree where each node in the tree holds a value of 0 or 1, beginning with a count of 1. |
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1
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| 1, 0, 2, 1, 4, 3, 8, 7, 16, 15, 32, 31, 64, 63, 128, 127, 256, 255, 512, 511, 1024, 1023, 2048, 2047, 4096, 4095, 8192, 8191, 16384, 16383, 32768, 32767, 65536, 65535, 131072, 131071, 262144, 262143, 524288, 524287, 1048576, 1048575, 2097152
(list; table; graph; listen)
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OFFSET
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0,3
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REFERENCES
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Douglas Comer, Ubiquitous B-Tree, ACM Computing Surveys (CSUR), (1979), Volume 11 Issue 2.
Huffman, D. A., A method for the construction of minimum redundancy codes, Proc. IRE 40 (1951), 1098-1101.
Knuth, D. E., Dynamic Huffman coding. J. Algorithms 6 (1985), 163-180.
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LINKS
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Barnes, G.C. et al., Balanced sample Binary Trees .
Fenwick, P.N. Cumulative Frequency.
Witteveen, C.Balanced Binary Trees .
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FORMULA
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-1/2*x^3+1/2*x^2-1/2+(x^4-3/2*x^2+1/2)*F(x) = 0
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MAPLE
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A106624 := proc(n) coeftayl( (1/2*x^3-1/2*x^2+1/2)/(x^4-3/2*x^2+1/2), x=0, n) ; end: seq(A106624(n), n=0..80) ; - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Feb 13 2008
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CROSSREFS
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Cf. A016116.
Cf. A014535, A037026, A058521, A058518, A058519, A058520.
Sequence in context: A087787 A100818 A005291 this_sequence A106622 A028297 A114438
Adjacent sequences: A106621 A106622 A106623 this_sequence A106625 A106626 A106627
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KEYWORD
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easy,nonn,tabl
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AUTHOR
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R. H. Barbour (bbarbour(AT)unitec.ac.nz), May 10 2005
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EXTENSIONS
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More terms from R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Feb 13 2008
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