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%I #50 Mar 05 2022 14:12:47
%S 1,8,23,77,281,1073,4193,16577,65921,262913,1050113,4197377,16783361,
%T 67121153,268460033,1073790977,4295065601,17180065793,68719869953,
%U 274878693377,1099513200641,4398049656833,17592192335873,70368756760577
%N a(n) = 4^(n+1) + 3*2^n + 1.
%H Vincenzo Librandi, <a href="/A036562/b036562.txt">Table of n, a(n) for n = -1..1000</a>
%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>
%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (7,-14,8).
%F a(n) = (1/2)*(A028401(n+4) + 1) for n > -1.
%F G.f.: (1+x-19*x^2+20*x^3)/(x*(1-x)*(1-2*x)*(1-4*x)). - _Colin Barker_, Mar 09 2012
%F a(n) = 7*a(n-1)-14*a(n-2)+8*a(n-3), for n>=3. - _Wesley Ivan Hurt_, Apr 26 2021
%t CoefficientList[Series[x*(1+x-19*x^2+20*x^3)/(x*(1-x)*(1-2*x)*(1-4*x)),{x,0,30}],x] (* _Vincenzo Librandi_, Apr 24 2012 *)
%o (Magma) [1]cat[4^(n+1)+3*2^n+1:n in [0..30]]; // _Vincenzo Librandi_, Apr 24 2012
%o (PARI) a(n)=4^(n+1)+3*2^n+1 \\ _Charles R Greathouse IV_, Apr 24 2012
%o (Python)
%o def a(n): return 1 if n == -1 else (pow(4,n+1)+3*pow(2,n)+1)
%o print([a(n) for n in range(-1, 100)]) # _Javier Rivera Romeu_, Mar 05 2022
%Y Sequences used for Shell sort: A003462, A033622, A036562, A036564, A036569, A055875, A055876.
%K nonn,easy
%O -1,2
%A _N. J. A. Sloane_
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