A116969 If n mod 2 = 0 then 3*2^(n-1)+n-1 else 3*2^(n-1)+n.

4, 7, 15, 27, 53, 101, 199, 391, 777, 1545, 3083, 6155, 12301, 24589, 49167, 98319, 196625, 393233, 786451, 1572883, 3145749, 6291477, 12582935, 25165847, 50331673, 100663321, 201326619, 402653211, 805306397, 1610612765, 3221225503, 6442450975, 12884901921

Offset: 1

Author

N. J. A. Sloane, Apr 01 2006

Keywords

• nonn
• easy

Comments

Number of moves to solve Easy Pagoda puzzle.

References

• Richard I. Hess, Compendium of Over 7000 Wire Puzzles, privately printed, 1991.
• Richard I. Hess, Analysis of Ring Puzzles, booklet distributed at 13th International Puzzle Party, Amsterdam, Aug 20 1993.

Links

• Index entries for linear recurrences with constant coefficients, signature (3,-1,-3,2).

Programs

Maple

f:=n-> if n mod 2 = 0 then 3*2^(n-1)+n-1 else 3*2^(n-1)+n; fi;

Mathematica

f[n_]:=If[EvenQ[n],3*2^(n-1)+n-1,3*2^(n-1)+n]; f/@Range[40] (* Harvey P. Dale, Sep 21 2012 *)

Formula

a(n) = 3*a(n-1)-a(n-2)-3*a(n-3)+2*a(n-4). G.f.: -x*(x^3-2*x^2-5*x+4) / ((x-1)^2*(x+1)*(2*x-1)). - Colin Barker, Jul 18 2013

Extensions

More terms from Colin Barker, Jul 18 2013