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%I #14 Sep 08 2022 08:45:50
%S 0,1,1,2,3,5,7,11,16,24,35,50,72,103,147,209,297,421,597,845,1196,
%T 1692,2393,3383,4782,6759,9552,13498,19073,26949,38077,53799,76011,
%U 107393,151729,214368,302865,427895,604538,854102
%N a(n) = a(n-1)+a(n-2)-Floor(a(n-3)/2)-Floor(a(n-8)/2); initial terms are 0, 1, 1, 2, 3, 5, 7, 11.
%C A two wave dying rabbits type sequence with limiting ratio 1.41280984879641.
%t f[-6] = 0; f[-5] = 0; f[-4] = 0; f[-3] = 0; f[-2] = 0; f[-1] = 0;
%t f[0] = 0; f[1] = 1;
%t f[n_] := f[n] = f[n - 1] + f[n - 2] - Floor[f[n - 3]/2] - Floor[f[n -8]/2];
%t Table[f[n], {n, 0, 30}]
%o (Magma) I:=[0, 1, 1, 2, 3, 5, 7, 11]; [ n le 8 select I[n] else Self(n-1)+Self(n-2)-(Self(n-3) div 2)-(Self(n-8) div 2): n in [1..40] ];
%Y Cf. A023438 (dying rabbits).
%K nonn
%O 0,4
%A _Roger L. Bagula_, Nov 22 2010
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