The OEIS is supported by the many generous donors to the OEIS Foundation.
%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