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A033622
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Good sequence of increments for Shell sort (best on big values).
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9
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1, 5, 19, 41, 109, 209, 505, 929, 2161, 3905, 8929, 16001, 36289, 64769, 146305, 260609, 587521, 1045505, 2354689, 4188161, 9427969, 16764929, 37730305, 67084289, 150958081, 268386305, 603906049, 1073643521, 2415771649, 4294770689
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OFFSET
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0,2
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COMMENTS
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One of the best sequences of gaps' lengths for Shell sort. Giving asymptotic O(N^4/3), therefore it is efficient in case of big N. On small values (apr. <4000) better use A108870, A102549. - Roman Dovgopol, May 8 2011
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REFERENCES
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J. Incerpi, R. Sedgewick, «Improved Upper Bounds for Shellsort», J. Computer and System Sciences 31, 2, 1985. - Roman Dovgopol, May 8 2011
D. E. Knuth, The Art of Computer Programming, Vol. 3, Sorting and Searching, 2nd ed, section 5.2. 1.
R. Sedgewick, J. Algorithms 7 (1986), 159-173 Addison-Wesley. ISBN 0-201-06672-6. - Roman Dovgopol, May 8 2011
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LINKS
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Nathaniel Johnston, Table of n, a(n) for n = 0..1000
Frank Ellermann, Comparison of Shell sorts based on EIS sequences.
Index entries for sequences related to sorting
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FORMULA
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a(n) = 9*2^n-9*2^(n/2)+1 if n is even;
a(n) = 8*2^n-6*2^((n+1)/2)+1 if n is odd.
G.f.: (8*x^4+2*x^3-8*x^2-4*x-1)/((x-1)*(2*x+1)*(2*x-1)*(2*x^2-1)). - Maksym Voznyy (voznyy(AT)mail.ru), Aug 11 2009
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MAPLE
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A033622 := proc(n) return (9-(n mod 2))*2^n-(9-3*(n mod 2))*2^ceil(n/2)+1: end: seq(A033622(n), n=0..29); # Nathaniel Johnston, May 08 2011
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PROG
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(C) int sedg(int i){ return (i%2) ? (9*(2<<i)-9*(2<<(i/2))+1) : (8*(2<<i)-6*(2<<((i+1)/2))+1); } (* Roman Dovgopol, May 8 2011 *)
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CROSSREFS
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Sequences used for Shell sort: A003462, A033622, A036562, A036564, A036569, A055875, A102549, A108870.
Sequence in context: A140761 A100572 A119534 * A091568 A147307 A089148
Adjacent sequences: A033619 A033620 A033621 * A033623 A033624 A033625
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KEYWORD
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nonn,easy
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AUTHOR
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Jud McCranie
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STATUS
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approved
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