%I #9 Nov 13 2017 03:13:02
%S 1,4,22,141,988,7337,56749,452332,3689697,30652931,258465558,
%T 2206330790,19029531220,165582392070,1451789520435,12813638048184,
%U 113755675163767,1015119850103821,9100463691522759,81923222827031025
%N Number of noncrossing connected graphs on n nodes on a circle having no four-sided faces.
%H Andrew Howroyd, <a href="/A045744/b045744.txt">Table of n, a(n) for n = 2..200</a>
%F a(n) = Sum_{i=0..floor((n-2)/3)} binomial(n-2+i, i)*binomial(4*n-4-i, n-2-3*i)/(n-1).
%o (PARI) a(n) = if(n>1, sum(i=0, floor((n-2)/3), binomial(n-2+i, i)*binomial(4*n-4-i, n-2-3*i))/(n-1)); \\ _Andrew Howroyd_, Nov 12 2017
%Y Column k=0 of A094046.
%Y Cf. A045743.
%K nonn
%O 2,2
%A _Emeric Deutsch_
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