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