cp's OEIS Frontend

A171997 a(n) = a(n-1) + a(n-2) - floor(a(n-2)/2) - floor(a(n-5)/2); initial terms are 1, 1, 2, 3, 4.

%I A171997 #27 Sep 08 2022 08:45:50
%S A171997 1,1,2,3,4,6,8,10,13,16,20,24,29,35,42,50,59,70,83,97,114,134,156,182,
%T A171997 212,246,285,330,382,441,509,588,678,781,900,1037,1193,1373,1580,1817,
%U A171997 2089,2402,2761,3172,3645,4187,4809,5523,6342,7282,8360
%N A171997 a(n) = a(n-1) + a(n-2) - floor(a(n-2)/2) - floor(a(n-5)/2); initial terms are 1, 1, 2, 3, 4.
%C A171997 lim_{n -> infinity} a(n+1)/a(n) = 1.14710876512065387719410850648860644150605499412513....
%C A171997 a(n) = A062435(n+2) for n < 15.
%t A171997 f[-3] = 0; f[-2] = 0; f[-1] = 0; f[0] = 1; f[1] = 1;
%t A171997 f[n_] := f[n] = f[n - 1] + f[n - 2] - Floor[f[n - 2]/2] - Floor[f[n - 5]/2]
%t A171997 Table[f[n], {n, 0, 50}]
%o A171997 (Magma) I:=[1,1,2,3,4]; [n le 5 select I[n] else Self(n-1) + Self(n-2) - Floor(Self(n-2)/2) - Floor(Self(n-5)/2): n in [1..60]]; // _Vincenzo Librandi_, Jun 24 2015
%Y A171997 Cf. A062435 (integer part of log(n!)^log(log(1 + n))), A023434 (a(n)=a(n-1)+a(n-2)-a(n-4)), A023435 (a(n)=a(n-1)+a(n-2)-a(n-5)), A023436 (a(n)=a(n-1)+a(n-2)-a(n-6)), A023437 (a(n)=a(n-1)+a(n-2)-a(n-7)), A023438 (a(n)=a(n-1)+a(n-2)-a(n-8)), A023439 (a(n)=a(n-1)+a(n-2)-a(n-9)), A023440 (a(n)=a(n-1)+a(n-2)+a(n-10)), A023441 (a(n)=a(n-1)+a(n-2)-a(n-11)), A023442 (a(n)=a(n-1)+a(n-2)-a(n-12)), A000044 (a(n)=a(n-1)+a(n-2)-a(n-13)), A173199 (a(n)=a(n-1)+a(n-2)-floor(a(n-3)/2)-floor(a(n-8)/2)).
%K A171997 nonn
%O A171997 1,3
%A A171997 _Roger L. Bagula_, Nov 22 2010
%E A171997 Offset changed from 0 to 1 by _Klaus Brockhaus_, Nov 29 2010