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%I #25 Aug 08 2023 07:22:01
%S 1,3,8,17,38,78,164,332,680,1368,2768,5552,11168,22368,44864,89792,
%T 179840,359808,720128,1440512,2882048,5764608,11531264,23063552,
%U 46131200,92264448,184537088,369078272,738172928,1476354048
%N Number of Greek-key tours on a 3 X n board; i.e., self-avoiding walks on a 3 X n grid starting in the top left corner.
%D Posting by Thomas Womack (mert0236(AT)sable.ox.ac.uk) to sci.math newsgroup, Apr 21 1999.
%H Robert Israel, <a href="/A046994/b046994.txt">Table of n, a(n) for n = 1..2985</a>
%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (2, 2, -4).
%F a(1) = 1; a(2m) = Sum_{i = 2...2m-1} a(i) + 3*2^(m-1); a(2m+1) = Sum_{i = 2...2m} a(i) + 5*2^(m-1).
%F a(n) = 11*2^(n-3) - (4 + (-1)^n)*(2^((1/4)*(2n - 7 - (-1)^n))), n >= 2. - _Nathaniel Johnston_, Feb 03 2006
%F a(n) = 2*a(n-1)+2*a(n-2)-4*a(n-3) for n>4. G.f.: x*(1+x-x^3)/(1-2*x-2*x^2+4*x^3). - _Colin Barker_, Jul 19 2012
%e On a 3 X 3 board labeled 123 456 789 (reading across rows), 125478963 is such a tour.
%p A046994:=n->`if`(n=1,1,11*2^(n-3)-(4+(-1)^n)*(2^((1/4)*(2*n-7-(-1)^n)))): seq(A046994(n), n=1..30); # _Wesley Ivan Hurt_, Sep 14 2014
%t CoefficientList[Series[(1 + x - x^3)/(1 - 2 x - 2 x^2 + 4 x^3), {x, 0, 30}], x] (* _Wesley Ivan Hurt_, Sep 14 2014 *)
%Y Cf. A046995.
%K nonn,walk
%O 1,2
%A Antreas P. Hatzipolakis (xpolakis(AT)otenet.gr)
%E More terms and formula from _Hugo van der Sanden_
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