A085839 a(0)=1, a(1)=3, a(n) = floor((Pi + 1/Pi)*a(n-1) - a(n-2)).

1, 3, 9, 28, 87, 273, 857, 2692, 8457, 26568, 83465, 262212, 823762, 2587924, 8130202, 25541782, 80241874, 252087281, 791955549, 2488001734, 7816287969, 24555592861, 77143670136, 242353987370, 761377506289, 2391937980365

Offset: 0

Author

Gary W. Adamson, Jul 05 2003

Keywords

• nonn

Comments

a(n+1)/a(n) converges to Pi.

Links

• Harvey P. Dale, Table of n, a(n) for n = 0..1000

Crossrefs

Cf. A000796, A085421, A085422.

Programs

Mathematica

a[n_] := a[n] = Floor[(Pi + 1/Pi)a[n - 1] - a[n - 2]]; Table[a[n], {n, 0, 25}] (* Robert G. Wilson v *)
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 *)

Extensions

Edited by Don Reble, Nov 14 2005

Definition corrected by Robert G. Wilson v, Apr 26 2006