%I #11 Mar 02 2025 21:31:03

%S 2,15,53,146,356,809,1759,3716,7702,15763,31993,64582,129912,260749,

%T 522627,1046616,2094858,4191639,8385533,16773690,33550412,67104305,

%U 134212583,268429676,536864446,1073734619,2147475649,4294958446,8589924832,17179858453

%N Number of minimal edge cuts in the 3 X n grid graph.

%H Andrew Howroyd, <a href="/A378933/b378933.txt">Table of n, a(n) for n = 1..200</a>

%H <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (6,-14,16,-9,2).

%F a(n) = 16*2^n - (2*n^3 + 9*n^2 + 73*n + 96)/6.

%F G.f.: x*(2 + 3*x - 9*x^2 + 6*x^3)/((1 - 2*x)*(1 - x)^4).

%F a(n) = A166761(n)/2.

%t LinearRecurrence[{6, -14, 16, -9, 2}, {2, 15, 53, 146, 356}, 30] (* _Paolo Xausa_, Mar 02 2025 *)

%o (PARI) a(n) = {16*2^n - (2*n^3 + 9*n^2 + 73*n + 96)/6}

%Y Row 3 of A378932.

%Y Cf. A166761, A359988, A378934.

%K nonn,easy

%O 1,1

%A _Andrew Howroyd_, Dec 11 2024