A116972 a(n) = 11*3^n - 2*n - 10.

1, 21, 85, 281, 873, 2653, 7997, 24033, 72145, 216485, 649509, 1948585, 5845817, 17537517, 52612621, 157837937, 473513889, 1420541749, 4261625333, 12784876089, 38354628361, 115063885181, 345191655645, 1035574967041

Offset

0,2

Comments

Number of moves to solve Type 3 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

Table of n, a(n) for n=0..23.

Index entries for linear recurrences with constant coefficients, signature (5,-7,3).

Formula

a(0)=1, a(n)=3*a(n-1)+4*n+14. - Zak Seidov, Apr 02 2006

a(0)=1, a(1)=21, a(2)=85, a(n)=5*a(n-1)-7*a(n-2)+3*a(n-3). G.f.: (1+16*x-13*x^2)/(1-5*x+7*x^2-3*x^3). [Colin Barker, Jan 25 2012]

Mathematica

f[n_] := 11*3^n - 2 n - 10; Array[f, 24, 0] (* or *)
CoefficientList[ Series[(13x^2 - 16x - 1)/((x - 1)^2 (3x - 1)), {x, 0, 23}], x] (* or *)
LinearRecurrence[{5, -7, 3}, {1, 21, 85}, 24] (* Robert G. Wilson v, Feb 01 2016 *)

Prog

(Magma) [11*3^n-2*n-10: n in [0..30]]; // Vincenzo Librandi, Feb 04 2016

Crossrefs

Sequence in context: A044208 A044589 A374527 * A221475 A277356 A041858

Adjacent sequences: A116969 A116970 A116971 * A116973 A116974 A116975

Keyword

nonn,easy

Author

N. J. A. Sloane, Apr 01 2006

Status

approved