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%I #15 Dec 30 2019 04:27:08
%S 2,5,22,75,264,941,3286,11623,40960,144267,508812,1792981,6319994,
%T 22277291,78518760,276763545,975517878,3438444583,12119670866,
%U 42718700667,150572583140,530730064095,1870688029160,6593699432859,23241110692298,81918995835971
%N Number of maximal matchings in the grid graph P_3 X P_n.
%H Andrew Howroyd, <a href="/A288028/b288028.txt">Table of n, a(n) for n = 1..200</a>
%H Svenja Huntemann, Neil A. McKay, <a href="https://arxiv.org/abs/1909.12419">Counting Domineering Positions</a>, arXiv:1909.12419 [math.CO], 2019.
%F Empirical: a(n) = a(n-1) +5*a(n-2) +11*a(n-3) +5*a(n-4) +14*a(n-5) +8*a(n-6) +3*a(n-7) -5*a(n-9) -11*a(n-10) -a(n-11) +2*a(n-12) +a(n-15) for n>15.
%F Empirical g.f.: x*(2 +3*x +7*x^2 +6*x^3 +14*x^4 +7*x^5 +4*x^6 -x^7 -5*x^8 - 11*x^9 -2*x^10 +2*x^11 +x^12 +x^14)/(1 -x -5*x^2 -11*x^3 -5*x^4 -14*x^5 - 8*x^6 -3*x^7 +5*x^9 +11*x^10 +x^11 -2*x^12 -x^15). - _Colin Barker_, Jun 11 2017
%Y Row 3 of A288026.
%Y Cf. A286945, A287595.
%K nonn
%O 1,1
%A _Andrew Howroyd_, Jun 04 2017