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%I #20 Oct 19 2020 12:27:44
%S 1,3,7,21,48,112,336,861,1968,4592,13776,33936,86961,198768,463792,
%T 1391376,3402672,8382192,21479367,49095696,114556624,343669872,
%U 852913488,2085837936,5138283696,13166851971,30095661648,70223210512
%N Increments used in Sedgewick-Incerpi upper bound for shell sort.
%D D. E. Knuth, The Art of Computer Programming, Vol. 3, Sorting and Searching, 2nd ed, section 5.2.1, pp. 91-92.
%H Robert Sedgewick, <a href="http://www.cs.princeton.edu/~rs/talks/shellsort.ps">Analysis of shellsort and related algorithms</a>, Fourth European Symposium on Algorithms, Barcelona, September, 1996.
%H <a href="/index/So#sorting">Index entries for sequences related to sorting</a>
%F 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.
%t A036569[k_] :=
%t With[{r = Floor[Sqrt[2 k + Sqrt[2 k]]]},
%t With[{b = r (r + 1)/2 - k + 1},
%t Times @@ (A036567 /@
%t Select[Range[r], # != b &])]]; (* _Morgan Owens_, Oct 08 2020 *)
%t Array[A036569, 10]
%Y Sequences used for Shell sort: A003462, A033622, A036562, A036564, A036569, A055875.
%K nonn
%O 0,2
%A _N. J. A. Sloane_
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