A085688 a(1) = 11; a(n) = if n == 2 mod 3 then a(n-1)-3, if n == 0 mod 3 then a(n-1)-2, if n == 1 mod 3 then a(n-1)*2.

11, 8, 6, 12, 9, 7, 14, 11, 9, 18, 15, 13, 26, 23, 21, 42, 39, 37, 74, 71, 69, 138, 135, 133, 266, 263, 261, 522, 519, 517, 1034, 1031, 1029, 2058, 2055, 2053, 4106, 4103, 4101, 8202, 8199, 8197, 16394, 16391, 16389, 32778, 32775, 32773, 65546, 65543, 65541, 131082

Offset: 1

Author

N. J. A. Sloane, Jul 18 2003

Keywords

• nonn
• easy

Comments

Sequence (in reversed order) was given as a puzzle: find the next term after 18, 9, 11, 14, 7, 9, 12! Thanks to Farideh Firoozbakht and Zak Seidov for the solution.

Links

• Harvey P. Dale, Table of n, a(n) for n = 1..1000
• Index entries for linear recurrences with constant coefficients, signature (0,0,3,0,0,-2).

Programs

Maple

a := proc(n) option remember; if n=1 then 11 elif n mod 3 = 2 then a(n-1)-3 elif n mod 3 = 0 then a(n-1)-2 else a(n-1)*2; fi; end;

Mathematica

a[1] = 11; a[n_] := (3 - (-1)^Mod[n, 3])/2*a[n - 1] - (1 + (-1)^Mod[n, 3])/2* Floor[Mod[n, 3]/2] - (-1)^Mod[n, 3] - 1 (* Farideh Firoozbakht, Jul 23 2003 *)
nxt[{n_,a_}]:=Module[{c=Mod[n+1,3]},{n+1,Which[c==2,a-3,c==0,a-2,c==1, 2a]}]; NestList[nxt,{1,11},60][[All,2]] (* or *) LinearRecurrence[ {0,0,3,0,0,-2},{11,8,6,12,9,7},70] (* Harvey P. Dale, Mar 14 2020 *)

Formula

a(1)=11; for k=>1, a(3k-1) = 7+2^(3k-1), a(3k) = 5+2^(3k-1), a(3k+1) = 10+2^(3k). - Zak Seidov, Jul 24 2003

a(n) = 2^floor((n-1)/3) + floor(21/(((n-1) mod 3)+2)). - Dean Hickerson, Jul 24 2003

G.f.: -x*(-11-8*x-6*x^2+21*x^3+15*x^4+11*x^5) / ( (x-1)*(2*x^3-1)*(1+x+x^2) ). - R. J. Mathar, Oct 20 2013