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Search: id:A033622
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| A033622 |
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Good sequence of increments for Shell sort. |
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+0
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
(list; graph; listen)
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OFFSET
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0,2
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REFERENCES
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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
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LINKS
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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.:(-1+8*x^4+2*x^3-8*x^2-4*x)/((-1+x)*(2*x+1)*(2*x-1)*(2*x^2-1)) [From Maksym Voznyy (voznyy(AT)mail.ru), Aug 11 2009]
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CROSSREFS
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Sequences used for Shell sort: A003462, A033622, A036562, A036564, A036569, A055875.
Sequence in context: A140761 A100572 A119534 this_sequence A091568 A147307 A089148
Adjacent sequences: A033619 A033620 A033621 this_sequence 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 (j.mccranie(AT)comcast.net)
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