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A302759 Number of total dominating sets in the n-Andrásfai graph.

%I A302759 #25 Aug 29 2025 09:49:31
%S A302759 1,11,131,1365,12883,113935,967455,8013983,65410751,529283583,
%T A302759 4261449727,34213027327,274240586751,2196272295935,17580376055807,
%U A302759 140687025184767,1125685164621823,9006288735567871,72053745778425855,576444534576513023,4611617848860868607
%N A302759 Number of total dominating sets in the n-Andrásfai graph.
%H A302759 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/AndrasfaiGraph.html">Andrásfai Graph</a>
%H A302759 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/TotalDominatingSet.html">Total Dominating Set</a>
%H A302759 <a href="/index/Rec#order_07">Index entries for linear recurrences with constant coefficients</a>, signature (23,-210,996,-2664,4032,-3200,1024).
%F A302759 a(n) = (8^(n + 1) + (2^n*(n - 2) - 4^(n + 1))*(3*n - 1))/16 - 1 for n > 1.
%F A302759 a(n) = 23*a(n-1) - 210*a(n-2) + 996*a(n-3) - 2664*a(n-4) + 4032*a(n-5) - 3200*a(n-6) + 1024*a(n-7) for n > 8.
%F A302759 G.f.: x*(-1 + 12*x - 88*x^2 + 334*x^3 - 706*x^4 + 928*x^5 - 672*x^6 + 256*x^7)/((-1 + 2*x)^3*(-1 + 4*x)^2*(1 - 9*x + 8*x^2)).
%F A302759 E.g.f.: (1 - 8*exp(x) + 4*exp(8*x) + exp(4*x)*(2 - 24*x) + 2*x + exp(2*x)*(1 - 4*x + 6*x^2))/8. - _Stefano Spezia_, Aug 29 2025
%t A302759 Join[{1}, Table[(8^(n + 1) + (2^n (n - 2) - 4^(n + 1) ) (3 n - 1) - 16)/16, {n, 2, 20}]]
%t A302759 Join[{1}, LinearRecurrence[{23, -210, 996, -2664, 4032, -3200, 1024}, {11, 131, 1365, 12883, 113935, 967455, 8013983}, 20]]
%t A302759 CoefficientList[Series[(-1 + 12 x - 88 x^2 + 334 x^3 - 706 x^4 + 928 x^5 - 672 x^6 + 256 x^7)/((-1 + 2 x)^3 (-1 + 4 x)^2 (1 - 9 x + 8 x^2)), {x, 0, 20}], x]
%Y A302759 Cf. A285272, A287429, A302762.
%K A302759 nonn,easy,changed
%O A302759 1,2
%A A302759 _Eric W. Weisstein_, Apr 12 2018
%E A302759 a(9)-a(21) from _Andrew Howroyd_, Apr 18 2018