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Number of minimal dominating sets in the n-book graph.
0

%I #13 Feb 16 2025 08:34:02

%S 6,7,11,19,35,67,131,259,515,1027,2051,4099,8195,16387,32771,65539,

%T 131075,262147,524291,1048579,2097155,4194307,8388611,16777219,

%U 33554435,67108867,134217731,268435459,536870915,1073741827,2147483651,4294967299,8589934595

%N Number of minimal dominating sets in the n-book graph.

%H Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/BookGraph.html">Book Graph</a>

%H Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/MinimalDominatingSet.html">Minimal Dominating Set</a>

%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (3,-2).

%F a(n) = A062709(n) = 2^n + 3 for n > 1.

%F G.f.: x*(6 - 11*x + 2*x^2)/((-1 + x)*(-1 + 2*x)).

%F E.g.f.: exp(x)*(3 + exp(x)) - 4 + x. - _Stefano Spezia_, Sep 04 2021

%t Join[{6}, 2^Range[2, 20] + 3]

%t CoefficientList[Series[(6 - 11 x + 2 x^2)/((-1 + x) (-1 + 2 x)), {x, 0, 20}], x]

%Y Cf. A062709 (essentially the same).

%K nonn,easy,changed

%O 1,1

%A _Eric W. Weisstein_, Sep 04 2021