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A303930 Number of no-leaf subgraphs of the 2 X n grid up to horizontal and vertical reflection.

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