OFFSET
2,2
COMMENTS
Number of moves to solve Type 1 Zig-Zag puzzle.
(3^(p+1) - 7)/2 = a(p+1) == 1 (mod p) since (3^(p-1) - 1)/2 = A003462(p-1) == 0 (mod p), for primes p > 7 (see comment by _Alexander Adamchuck_ in A003462); in addition, a(4) == 1 (mod 3) and a(6) == 1 (mod 5). - Hartmut F. W. Hoft, Aug 22 2018
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
FORMULA
a(n) = 3*a(n-1) + 7 with n > 2, a(2)=1. - Vincenzo Librandi, Aug 02 2010
a(2)=1, a(3)=10; for n > 3, a(n) = 4*a(n-1) - 3*a(n-2). - Harvey P. Dale, Jan 17 2013
G.f.: x^2*(1+6*x)/((1-3*x)*(1-x)). - Vincenzo Librandi, Mar 30 2015
From Hartmut F. W. Hoft, Aug 22 2018: (Start)
a(2) = 1; a(n) = a(n-1) + 3^(n-1) for n > 2. -
a(n) = A003462(n) - 3, n >= 2. (End)
MAPLE
a[1]:=1:for n from 2 to 50 do a[n]:=3^n+a[n-1] od: seq(a[n], n=1..25); # Zerinvary Lajos, Mar 09 2008
MATHEMATICA
Table[(3^n - 7)/2, {n, 2, 30}] (* Stefan Steinerberger, Apr 02 2006 *)
LinearRecurrence[{4, -3}, {1, 10}, 30] (* Harvey P. Dale, Jan 17 2013 *)
CoefficientList[Series[(1 + 6 x) / ((1 - 3 x) (1 - x)), {x, 0, 33}], x] (* Vincenzo Librandi, Mar 30 2015 *)
PROG
(PARI) a(n)=(3^n-7)/2 \\ Charles R Greathouse IV, Sep 04 2014
(Magma) [(3^n-7)/2: n in [2..30]]; // Vincenzo Librandi, Mar 30 2015
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
N. J. A. Sloane, Apr 01 2006
STATUS
approved