Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).
%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