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Number of minimal total dominating sets in the n-Andrásfai graph.
1

%I #17 Feb 09 2024 03:59:51

%S 1,5,14,44,112,238,449,782,1287,2030,3096,4592,6650,9430,13123,17954,

%T 24185,32118,42098,54516,69812,88478,111061,138166,170459,208670,

%U 253596,306104,367134,437702,518903,611914,717997,838502,974870,1128636,1301432,1494990,1711145

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

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

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

%H <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (6,-15,20,-15,6,-1).

%F a(n) = (-720 + 2732*n - 1880*n^2 + 505*n^3 - 40*n^4 + 3*n^5)/120 for n > 2.

%F a(n) = 6*a(n-1) - 15*a(n-2) + 20*a(n-3) - 15*a(n-4) + 6*a(n-5) - a(n-6) for n > 8.

%F G.f.: x*(1 - x - x^2 + 15*x^3 - 27*x^4 + 15*x^5 + 2*x^6 - x^7)/(-1 + x)^6.

%t Join[{1, 5}, Table[(-720 + 2732 n - 1880 n^2 + 505 n^3 - 40 n^4 + 3 n^5)/120, {n, 3, 20}]

%t Join[{1, 5}, LinearRecurrence[{6, -15, 20, -15, 6, -1}, {14, 44, 112, 238, 449, 7827}, 20]]

%t CoefficientList[Series[(1 - x - x^2 + 15 x^3 - 27 x^4 + 15 x^5 + 2 x^6 - x^7)/(-1 + x)^6, {x, 0, 20}], x]

%Y Cf. A213661, A290270, A302603.

%K nonn,easy

%O 1,2

%A _Eric W. Weisstein_, Apr 12 2018

%E a(8)-a(20) from _Andrew Howroyd_, Apr 15 2018