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%I #24 Aug 10 2020 02:23:55
%S 1,17,205,2129,20341,184457,1615405,13808609,116015461,962575097,
%T 7913168605,64610052689,524855128981,4247421698537,34274519697805,
%U 275985344786369,2218709434248901,17815093293410777,142915542082163005,1145704555158361649,9179974972732223221
%N Number of 3 X n {0,1}-matrices such that: (a) first and second row have a common 1, (b) second and third row have a common 1.
%H Andi Fugard, <a href="https://www.andifugard.info/wp-content/uploads/2020/08/Fugard-2008-Counting-first-order-models-with-n-individuals-of-syllogisms.pdf">Counting first-order models (with n individuals) of syllogisms</a>.
%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (19,-118,240).
%F a(n) = 8^n-2*6^n+5^n.
%F G.f.: x*(2*x-1)/((5*x-1)*(6*x-1)*(8*x-1)). [_Colin Barker_, Nov 05 2012]
%Y Cf. A051588.
%K easy,nonn
%O 1,2
%A _Andi Fugard_, _Vladeta Jovovic_, Jul 26 2008
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