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Search: id:A106624
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| A106624 |
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G.f.: (1-x^2+x^3)/(1-3*x^2+2*x^4). |
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+0
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; graph; listen)
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OFFSET
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0,3
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COMMENT
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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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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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Index entries for sequences related to linear recurrences with constant coefficients
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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a(n) = 2^floor(n/2) + [(-1)^n - 1]/2. - N. J. A. Sloane (njas(AT)research.att.com), May 15 2005
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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, A014535, A037026, A058521, A058518, A058519, A058520.
Sequence in context: A087787 A100818 A005291 this_sequence A028297 A114438 A109195
Adjacent sequences: A106621 A106622 A106623 this_sequence A106625 A106626 A106627
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KEYWORD
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easy,nonn
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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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New definition from N. J. A. Sloane (njas(AT)research.att.com), May 15 2008
More terms from R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Feb 13 2008
Edited by N. J. A. Sloane (njas(AT)research.att.com), Aug 29 2008 at the suggestion of R. J. Mathar
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