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%I #11 Sep 06 2023 16:13:31
%S 1,1,6,28,85,201,406,736,1233,1945,2926,4236,5941,8113,10830,14176,
%T 18241,23121,28918,35740,43701,52921,63526,75648,89425,105001,122526,
%U 142156,164053,188385,215326,245056,277761,313633,352870,395676,442261,492841,547638,606880
%N Number of minimal total dominating sets in the n-barbell graph.
%C Extended to a(1)-a(2) using the formula/recurrence.
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/BarbellGraph.html">Barbell 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_05">Index entries for linear recurrences with constant coefficients</a>, signature (5,-10,10,-5,1).
%F a(n) = (2 + (n - 3)*n*(n + 1)/4)*n.
%F G.f.: x*(-1 + 4*x - 11*x^2 + 2*x^3)/(-1 + x)^5.
%F a(n) = 5*a(n-1) - 10*a(n-2) + 10*a(n-3) - 5*a(n-4) + a(n-5).
%F E.g.f.: exp(x)*x*(4 - 2*x + 4*x^2 + x^3)/4. - _Stefano Spezia_, Sep 06 2023
%t Table[(2 + (n - 3) n (n + 1)/4) n, {n, 20}]
%t LinearRecurrence[{5, -10, 10, -5, 1}, {1, 1, 6, 28, 85}, 20]
%t CoefficientList[Series[(-1 + 4 x - 11 x^2 + 2 x^3)/(-1 + x)^5, {x, 0, 20}], x]
%o (Magma) [(2 + (n - 3)*n*(n + 1)/4)*n : n in [1..50]]; // _Wesley Ivan Hurt_, Apr 25 2023
%K nonn,easy
%O 1,3
%A _Eric W. Weisstein_, Apr 11 2018
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