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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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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
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OFFSET
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0,3
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COMMENTS
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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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Vincenzo Librandi, Table of n, a(n) for n = 0..5000
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, 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, Feb 13 2008
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PROG
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(MAGMA) [2^Floor(n/2) + Floor((-1)^n - 1)/2: n in [0..50]]; // Vincenzo Librandi, Aug 17 2011
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CROSSREFS
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Cf. A016116, A014535, A037026, A058521, A058518, A058519, A058520.
Sequence in context: A182712 A100818 A005291 * A028297 A207537 A114438
Adjacent sequences: A106621 A106622 A106623 * 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, May 15 2008
More terms from R. J. Mathar, Feb 13 2008
Edited by N. J. A. Sloane, Aug 29 2008 at the suggestion of R. J. Mathar
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STATUS
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approved
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