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%I #21 Dec 18 2022 02:33:15
%S 1,1,1,2,2,3,4,4,6,6,7,9,8,11,11,12,15,14,18,18,20,23,22,27,26,29,32,
%T 31,37,36,39,44,41,50,48,51,59,52,66,61,65,76,64,85,75,81,96,76,108,
%U 90,99
%N a(n) = a(n-2) + a(n-3) - floor(a(n-4)/2) - floor(a(n-6)/2).
%C The first negative term is a(82) = -69.
%H Harvey P. Dale, <a href="/A173332/b173332.txt">Table of n, a(n) for n = 0..1000</a>
%t f[-4] = 0; f[-3] = 0; f[-2] = 0; f[-1] = 0; f[0] = 1; f[1] = 1;
%t f[n_] := f[n] = f[n - 2] + f[n - 3] - Floor[f[n - 4]/2] - Floor[f[n - 6]/2]
%t Table[f[n], {n, 0, 50}]
%t nxt[{a_,b_,c_,d_,e_,f_}]:= {b,c,d,e,f,e+d-Floor[c/2]-Floor[a/2]}; NestList[ nxt,{1,1,1,2,2,3},50][[All,1]] (* _Harvey P. Dale_, Sep 18 2020 *)
%K sign,easy
%O 0,4
%A _Roger L. Bagula_, Nov 22 2010