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 A106624 Expansion of g.f.: (1 - x^2 + x^3)/((1-x^2)*(1-2*x^2)). 1
 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; refs; listen; history; text; internal format)
 OFFSET 0,3 COMMENTS 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. REFERENCES 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. LINKS Vincenzo Librandi, Table of n, a(n) for n = 0..5000 G. C. Barnes et al., Balanced sample Binary Trees, ACM SIGCSE Bulletin, Volume 37 Issue 1, 2005 pp. 166-170. P. N. Fenwick, Cumulative Frequency, Software: Practice and Experience, 1994. C. Witteveen, Balanced Binary Trees, Slides. Index entries for linear recurrences with constant coefficients, signature (0,3,0,-2). FORMULA a(n) = 2^floor(n/2) + floor((-1)^n - 1)/2. - N. J. A. Sloane, May 15 2005 MAPLE A106624 := proc(N)     2^floor(n/2)+((-1)^n-1)/2 ; end proc: seq(A106624(n), n=0..20) ; # R. J. Mathar, Apr 14 2018 MATHEMATICA Table[2^Floor[n/2] +Floor[(-1)^n-1]/2, {n, 0, 50}] (* G. C. Greubel, Feb 19 2019 *) PROG (Magma) [2^Floor(n/2) + Floor((-1)^n - 1)/2: n in [0..50]]; // Vincenzo Librandi, Aug 17 2011 (PARI) vector(50, n, n--; 2^floor(n/2) +floor((-1)^n-1)/2) \\ G. C. Greubel, Feb 19 2019 (Sage) [2^floor(n/2) +floor((-1)^n-1)/2 for n in (0..50)] # G. C. Greubel, Feb 19 2019 CROSSREFS Cf. A016116, A014535, A037026, A058518 - A058521, A000079 (bisection), A000225 (bisection). Sequence in context: A182712 A100818 A005291 * A028297 A207537 A114438 Adjacent sequences:  A106621 A106622 A106623 * A106625 A106626 A106627 KEYWORD easy,nonn,changed AUTHOR Robert H Barbour, May 10 2005 EXTENSIONS New definition from N. J. A. Sloane, May 15 2008 Edited by N. J. A. Sloane, Aug 29 2008 at the suggestion of R. J. Mathar STATUS approved

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Last modified September 27 15:39 EDT 2022. Contains 357062 sequences. (Running on oeis4.)