Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).
%I #19 Apr 11 2021 01:28:54
%S 1,3,9,28,87,273,857,2692,8457,26568,83465,262212,823762,2587924,
%T 8130202,25541782,80241874,252087281,791955549,2488001734,7816287969,
%U 24555592861,77143670136,242353987370,761377506289,2391937980365
%N a(0)=1, a(1)=3, a(n) = floor((Pi + 1/Pi)*a(n-1) - a(n-2)).
%C a(n+1)/a(n) converges to Pi.
%H Harvey P. Dale, <a href="/A085839/b085839.txt">Table of n, a(n) for n = 0..1000</a>
%t a[n_] := a[n] = Floor[(Pi + 1/Pi)a[n - 1] - a[n - 2]]; Table[a[n], {n, 0, 25}] (* _Robert G. Wilson v_ *)
%t nxt[{a_,b_}]:=Module[{c=Pi+1/Pi},{b,Floor[b*c-a]}]; NestList[nxt,{1,3},30][[All,1]] (* _Harvey P. Dale_, Oct 07 2018 *)
%Y Cf. A000796, A085421, A085422.
%K nonn
%O 0,2
%A _Gary W. Adamson_, Jul 05 2003
%E Edited by _Don Reble_, Nov 14 2005
%E Definition corrected by _Robert G. Wilson v_, Apr 26 2006