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%I #19 Sep 08 2022 08:45:24
%S 10,56,242,988,3974,15920,63706,254852,1019438,4077784,16311170,
%T 65244716,260978902,1043915648,4175662634,16702650580,66810602366,
%U 267242409512,1068969638098,4275878552444,17103514209830,68414056839376
%N a(n) = (35*2^((2*(3*n+2) + 2)/3) - 2*(3*n+2) - 46)/9.
%C Number of moves to solve Type 2 Zig-Zag puzzle.
%D Richard I. Hess, Compendium of Over 7000 Wire Puzzles, privately printed, 1991.
%D Richard I. Hess, Analysis of Ring Puzzles, booklet distributed at 13th International Puzzle Party, Amsterdam, Aug 20 1993.
%H Vincenzo Librandi, <a href="/A116971/b116971.txt">Table of n, a(n) for n = 0..1000</a>
%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (6,-9,4).
%F 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]
%t Table[(35*2^((2*(3*n + 2) + 2)/3) - 2*(3*n + 2) - 46)/9, {n, 0, 30}] (* _Stefan Steinerberger_, Apr 02 2006 *)
%t LinearRecurrence[{6,-9,4},{10,56,242},30] (* _Harvey P. Dale_, Sep 08 2021 *)
%o (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
%K nonn,easy
%O 0,1
%A _N. J. A. Sloane_, Apr 01 2006
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