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 A116970 a(n) = (3^n - 7)/2. 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 (list; graph; refs; listen; history; text; internal format)
 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 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. Sequence in context: A200872 A212755 A048480 * A199208 A110528 A208674 Adjacent sequences:  A116967 A116968 A116969 * A116971 A116972 A116973 KEYWORD nonn,easy AUTHOR N. J. A. Sloane, Apr 01 2006 STATUS approved

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Last modified November 29 01:03 EST 2020. Contains 338755 sequences. (Running on oeis4.)