A116971 a(n) = (35*2^((2*(3*n+2) + 2)/3) - 2*(3*n+2) - 46)/9.

10, 56, 242, 988, 3974, 15920, 63706, 254852, 1019438, 4077784, 16311170, 65244716, 260978902, 1043915648, 4175662634, 16702650580, 66810602366, 267242409512, 1068969638098, 4275878552444, 17103514209830, 68414056839376

Offset

0,1

Comments

Number of moves to solve Type 2 Zig-Zag 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

Vincenzo Librandi, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (6,-9,4).

Formula

a(n) = 6*a(n-1)-9*a(n-2)+4*a(n-3). G.f.: 2*(5-2*x-2*x^2)/((1-x)^2*(1-4*x)). [Colin Barker, Sep 09 2012]

Mathematica

Table[(35*2^((2*(3*n + 2) + 2)/3) - 2*(3*n + 2) - 46)/9, {n, 0, 30}] (* Stefan Steinerberger, Apr 02 2006 *)
LinearRecurrence[{6, -9, 4}, {10, 56, 242}, 30] (* Harvey P. Dale, Sep 08 2021 *)

Prog

(Magma) [Round((35*2^((2*(3*n + 2) + 2)/3 ) - 2*(3*n + 2) - 46)/9): n in [0..25]] // Vincenzo Librandi, Sep 09 2012

Crossrefs

Sequence in context: A055911 A087076 A014483 * A200054 A034195 A351458

Adjacent sequences: A116968 A116969 A116970 * A116972 A116973 A116974

Keyword

nonn,easy

Author

N. J. A. Sloane, Apr 01 2006

Status

approved