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%I #25 Oct 06 2018 14:30:13
%S 1,2,4,10,26,76,232,750,2493,8514,29524,103708,367225,1308542,4682276,
%T 16807286,60462082,217855460,785863048,2837177434,10249053629,
%U 37039804078,133902392980,484178868612,1751030978481,6333341963706,22909148647012,82872738727330
%N Number of no-leaf subgraphs of the 2 X n grid up to horizontal and vertical reflection.
%C The limit lim_{n -> infinity} A020876(n - 1)/a(n) = 4.
%H Peter Kagey, <a href="/A303930/b303930.txt">Table of n, a(n) for n = 1..1000</a>
%F Conjectures from _Colin Barker_, May 03 2018: (Start)
%F G.f.: x*(1 - 6*x + 4*x^2 + 30*x^3 - 45*x^4 - 22*x^5 + 60*x^6 - 20*x^7) / ((1 - 3*x + x^2)*(1 - 5*x + 5*x^2)*(1 - 5*x^2 + 5*x^4)).
%F a(n) = 8*a(n-1) - 16*a(n-2) - 20*a(n-3) + 95*a(n-4) - 60*a(n-5) - 80*a(n-6) + 100*a(n-7) - 25*a(n-8) for n>8.
%F (End)
%e For n = 4 the a(4) = 10 subgraphs of the 2 X 4 grid are:
%e + + + + +---+ + + + +---+ +
%e | | | |
%e + + + +, +---+ + +, + +---+ +,
%e +---+ +---+ +---+---+ + +---+---+---+
%e | | | | | | | | |
%e +---+ +---+, +---+---+ +, +---+---+---+,
%e +---+---+---+ +---+---+---+ +---+---+---+
%e | | | | | | | | | |
%e +---+---+---+, +---+---+---+, +---+ +---+, and
%e +---+---+ +
%e | | |
%e +---+---+ +.
%Y Cf. A020876, A301976.
%Y A093129 is analogous for 2 X (n+1) grids where reflections are considered distinct.
%K nonn
%O 1,2
%A _Peter Kagey_, May 02 2018
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