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A116970
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a(n) = (3^n - 7)/2.
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4
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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
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OFFSET
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2,2
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COMMENTS
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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
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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(2)=1, a(3)=10; for n > 3, a(n) = 4*a(n-1) - 3*a(n-2). - Harvey P. Dale, Jan 17 2013
a(2) = 1; a(n) = a(n-1) + 3^(n-1) for n > 2. -
a(n) = A003462(n) - 3, n >= 2. (End)
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MAPLE
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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
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MATHEMATICA
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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 *)
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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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