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A116972
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a(n) = 11*3^n - 2*n - 10.
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0
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1, 21, 85, 281, 873, 2653, 7997, 24033, 72145, 216485, 649509, 1948585, 5845817, 17537517, 52612621, 157837937, 473513889, 1420541749, 4261625333, 12784876089, 38354628361, 115063885181, 345191655645, 1035574967041
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history;
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OFFSET
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0,2
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COMMENTS
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Number of moves to solve Type 3 Zig-Zag puzzle.
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REFERENCES
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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.
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LINKS
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FORMULA
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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]
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MATHEMATICA
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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 *)
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PROG
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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