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

0,2

Comments

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

Links

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

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 *)

Crossrefs

Cf. A000796, A085421, A085422.

Sequence in context: A263841 A052939 A225114 * A115239 A134915 A339064

Adjacent sequences: A085836 A085837 A085838 * A085840 A085841 A085842

Keyword

nonn

Author

Gary W. Adamson, Jul 05 2003

Extensions

Edited by Don Reble, Nov 14 2005

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

Status

approved