A116970 a(n) = (3^n - 7)/2.

1, 10, 37, 118, 361, 1090, 3277, 9838, 29521, 88570, 265717, 797158, 2391481, 7174450, 21523357, 64570078, 193710241, 581130730, 1743392197, 5230176598, 15690529801, 47071589410, 141214768237, 423644304718, 1270932914161

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

Table of n, a(n) for n=2..26.

Index entries for linear recurrences with constant coefficients, signature (4,-3).

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

Cf. A003462, A063679.

Sequence in context: A200872 A212755 A048480 * A355044 A199208 A110528

Adjacent sequences: A116967 A116968 A116969 * A116971 A116972 A116973

Keyword

nonn,easy

Author

N. J. A. Sloane, Apr 01 2006

Status

approved