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A116972
a(n) = 11*3^n - 2*n - 10.
0
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.
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
KEYWORD
nonn,easy
AUTHOR
N. J. A. Sloane, Apr 01 2006
STATUS
approved