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%I #13 Oct 03 2024 08:05:14
%S 3,9,39,177,783,3369,14199,58977,242463,989529,4017159,16245777,
%T 65514543,263652489,1059392919,4251920577,17050729023,68332056249,
%U 273715645479,1096024843377,4387586157903,17560804984809,70274600998839,281192547174177,1125052618233183
%N Number of connected dominating sets in the 2 X n rook graph.
%H Andrew Howroyd, <a href="/A360876/b360876.txt">Table of n, a(n) for n = 1..1000</a>
%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (8,-19,12).
%F a(n) = 8*a(n-1) - 19*a(n-2) + 12*a(n-3) for n > 3.
%F G.f.: 3*x*(1 - 5*x + 8*x^2)/((1 - x)*(1 - 3*x)*(1 - 4*x)).
%t LinearRecurrence[{8, -19, 12}, {3, 9, 39}, 30] (* _Paolo Xausa_, Oct 03 2024 *)
%o (PARI) Vec(3*(1 - 5*x + 8*x^2)/((1 - x)*(1 - 3*x)*(1 - 4*x)) + O(x^25))
%Y Row 2 of A360875.
%Y Cf. A360874.
%K nonn,easy
%O 1,1
%A _Andrew Howroyd_, Feb 24 2023