A360876 Number of connected dominating sets in the 2 X n rook graph.
3, 9, 39, 177, 783, 3369, 14199, 58977, 242463, 989529, 4017159, 16245777, 65514543, 263652489, 1059392919, 4251920577, 17050729023, 68332056249, 273715645479, 1096024843377, 4387586157903, 17560804984809, 70274600998839, 281192547174177, 1125052618233183
Offset: 1
Links
- Andrew Howroyd, Table of n, a(n) for n = 1..1000
- Index entries for linear recurrences with constant coefficients, signature (8,-19,12).
Programs
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Mathematica
LinearRecurrence[{8, -19, 12}, {3, 9, 39}, 30] (* Paolo Xausa, Oct 03 2024 *) -
PARI
Vec(3*(1 - 5*x + 8*x^2)/((1 - x)*(1 - 3*x)*(1 - 4*x)) + O(x^25))
Formula
a(n) = 8*a(n-1) - 19*a(n-2) + 12*a(n-3) for n > 3.
G.f.: 3*x*(1 - 5*x + 8*x^2)/((1 - x)*(1 - 3*x)*(1 - 4*x)).