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A036569
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Increments used in Sedgewick-Incerpi upper bound for shell sort.
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12
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1, 3, 7, 21, 48, 112, 336, 861, 1968, 4592, 13776, 33936, 86961, 198768, 463792, 1391376, 3402672, 8382192, 21479367, 49095696, 114556624, 343669872, 852913488, 2085837936, 5138283696, 13166851971, 30095661648, 70223210512
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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, pp. 91-92.
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LINKS
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FORMULA
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a(0)=1, then a(s)=a(s-r)*b(r) for r such that C(r, 2)<s<=C(r+1, 2), where b() is A036567.
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MATHEMATICA
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With[{r = Floor[Sqrt[2 k + Sqrt[2 k]]]},
With[{b = r (r + 1)/2 - k + 1},
Select[Range[r], # != b &])]]; (* Morgan Owens, Oct 08 2020 *)
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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