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%I #36 Sep 08 2022 08:45:00
%S 2,3,5,6,10,11,18,19,30,31,47,48,70,71,100,101,138,139,185,186,242,
%T 243,310,311,390,391,483,484,590,591,712,713,850,851,1005,1006,1178,
%U 1179,1370,1371,1582,1583,1815,1816,2070,2071,2348,2349,2650,2651
%N a(n) = n+1 + ceiling(n/2)*(ceiling(n/2)-1)*(ceiling(n/2)+1)/6.
%H Vincenzo Librandi, <a href="/A053436/b053436.txt">Table of n, a(n) for n = 1..5000</a>
%H G. Giani, K. Strassburger, <a href="http://dx.doi.org/10.1016/S0378-3758(99)00104-4">Multiple comparison procedures for optimally discriminating between good, equivalent and bad treatments with respect to a control</a>, J. Statist. Planning Infer. 83 (No. 2, 2000), 413-440.
%H <a href="/index/Rec#order_07">Index entries for linear recurrences with constant coefficients</a>, signature (1,3,-3,-3,3,1,-1).
%F a(n) = n + 1 + A000292(ceiling(n/2)-2).
%F a(n) = a(n-1) +3 a(n-2) -3 a(n-3) -3 a(n-4) +3 a(n-5) +a(n-6) -a(n-7). - _R. J. Mathar_, Mar 11 2012
%F G.f.: x*(2+x-4*x^2-2*x^3+4*x^4+x^5-x^6)/((1-x)^4*(1+x)^3). - _Colin Barker_, Apr 02 2012
%F a(n) = (2*n^3+3*n^2+91*n+93-3*(n^2+n-1)*(-1)^n)/96. - _Luce ETIENNE_, Oct 22 2014
%t CoefficientList[Series[(2+x-4*x^2-2*x^3+4*x^4+x^5-x^6)/((1-x)^4*(1+x)^3),{x,0,50}],x] (* _Vincenzo Librandi_, Apr 28 2012 *)
%t cn[n_]:=(Times@@(Ceiling[n/2]+{1,0,-1}))/6+n+1; Array[cn,50] (* or *) LinearRecurrence[{1,3,-3,-3,3,1,-1},{2,3,5,6,10,11,18},50] (* _Harvey P. Dale_, Mar 27 2013 *)
%o (Magma) [n+1 + Ceiling(n/2)*(Ceiling(n/2)-1)*(Ceiling(n/2)+1)/6: n in [1..50]]; // _Vincenzo Librandi_, Apr 28 2012
%o (PARI) for(n=1,30, print1((2*n^3+3*n^2+91*n+93-3*(n^2+n-1)*(-1)^n)/96, ", ")) \\ _G. C. Greubel_, May 26 2018
%Y Cf. A000292.
%K easy,nonn
%O 1,1
%A Klaus Strassburger (strass(AT)ddfi.uni-duesseldorf.de), Jan 11 2000
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