cp's OEIS Frontend

A071995 a(1) = 1, a(2) = 0, a(n) = a(floor(n/3)) + a(n - floor(n/3)).

%I A071995 #24 Jan 02 2022 17:12:51
%S A071995 1,0,1,2,3,2,3,2,3,4,3,4,5,6,7,6,7,6,7,8,9,10,9,8,9,8,9,10,11,12,13,
%T A071995 14,13,12,11,12,13,12,13,14,15,16,17,18,19,20,21,20,19,18,19,18,19,18,
%U A071995 19,18,19,20,21,22,23,24,25,26,27,28,29,30,29,30,29,28,27,26,27,28,27,26
%N A071995 a(1) = 1, a(2) = 0, a(n) = a(floor(n/3)) + a(n - floor(n/3)).
%C A071995 "Rauzy's sequence" with initial values 1, 0.
%C A071995 David Moews showed that a(n)/n converges to about 0.37512. - _Jim Nastos_, Jan 08 2003
%C A071995 Difference of consecutive terms is always +/- 1.
%H A071995 Gheorghe Coserea, <a href="/A071995/b071995.txt">Table of n, a(n) for n = 1..10000</a>
%H A071995 David Moews, <a href="http://djm.cc/dmoews/rauzy.pdf">Asymptotic behavior of Rauzy's sequence</a>
%H A071995 Jeffrey Shallit, <a href="http://www.cs.uwaterloo.ca/~shallit/Talks/pmc2.ps">Ten Problems I Can't Solve (1.1 MB ps)</a>
%t A071995 a[1]=1; a[2]=0; a[n_] := a[n]=a[Floor[n/3]]+a[n-Floor[n/3]]; Table[a[n], {n, 1, 80}]
%o A071995 (PARI)
%o A071995 n = 33; v = vector(n); v[1] = 'x; v[2] = 'y;
%o A071995 for(i = 3, n, v[i] = v[floor(i/3)] + v[i - floor(i/3)]);
%o A071995 apply(e -> polcoeff(e, 1, v[1]), v) \\ _Gheorghe Coserea_, Aug 22 2015
%Y A071995 Cf. A071991, A071996.
%K A071995 easy,nonn
%O A071995 1,4
%A A071995 _Jim Nastos_, Jun 17 2002
%E A071995 Edited by _Robert G. Wilson v_, Jun 23 2002