OFFSET
1,1
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).
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
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 (from 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 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
N. J. A. Sloane, Jul 18 2003
STATUS
approved