%I #42 Jan 05 2018 14:25:58
%S 5,57,489,4125,35117,299681,2557605,21826045,186255781,1589441093,
%T 13563736693,115748216413,987755062201,8429158472781,71931509371765,
%U 613838505628281,5238284505542721,44701699729693429,381468772192258129,3255321946095461785,27779786302899765081
%N Number of legal Go positions on a 2 X n board.
%H Colin Barker, <a href="/A266278/b266278.txt">Table of n, a(n) for n = 1..1000</a>
%H John Tromp, <a href="http://tromp.github.io/go/L2.html">Number of legal 2xn Go positions</a>
%H J. Tromp and G. Farnebäck, <a href="http://dx.doi.org/10.1007/978-3-540-75538-8_8">Combinatorics of Go</a>, Lecture Notes in Computer Science, 4630, 84-99, 2007.
%H <a href="/index/Rec#order_07">Index entries for linear recurrences with constant coefficients</a>, signature (10,-16,31,-13,20,2,-1).
%F a(n) = 10*a(n-1)-16*a(n-2)+31*a(n-3)-13*a(n-4)+20*a(n-5)+2*a(n-6)-a(n-7).
%F G.f.: x*(1 + x)^2*(5 - 3*x - 5*x^3 - x^4) / ((1 + x^2)*(1 - 10*x + 15*x^2 - 21*x^3 - 2*x^4 + x^5)). - _Colin Barker_, Jan 05 2018
%e For n = 1, the a(1) = 5 legal 2 X 1 boards are .. X. O. .X .O
%o (PARI) Vec(x*(1 + x)^2*(5 - 3*x - 5*x^3 - x^4) / ((1 + x^2)*(1 - 10*x + 15*x^2 - 21*x^3 - 2*x^4 + x^5)) + O(x^40)) \\ _Colin Barker_, Jan 05 2018
%Y Cf. A094777, A102620.
%K nonn,easy
%O 1,1
%A _Felix Fröhlich_, Dec 26 2015
%E Corrected and edited by _John Tromp_, Jan 26 2016