cp's OEIS Frontend

A347650 Number of minimum total dominating sets in the n-pan graph (for n > 2).

%I A347650 #10 Jun 11 2025 17:01:15
%S A347650 1,2,3,2,3,8,5,2,5,18,7,2,7,32,9,2,9,50,11,2,11,72,13,2,13,98,15,2,15,
%T A347650 128,17,2,17,162,19,2,19,200,21,2,21,242,23,2,23,288,25,2,25,338,27,2,
%U A347650 27,392,29,2,29,450,31,2,31,512,33,2,33,578,35,2,35,648
%N A347650 Number of minimum total dominating sets in the n-pan graph (for n > 2).
%C A347650 Sequence extended to a(1) using the formula/recurrence.
%C A347650 The total domination number is given by A004524(n + 2). - _Andrew Howroyd_, Jun 11 2025
%H A347650 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/PanGraph.html">Pan Graph</a>.
%H A347650 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/MinimumTotalDominatingSet.html">Minimum Total Dominating Set</a>.
%H A347650 <a href="/index/Rec#order_12">Index entries for linear recurrences with constant coefficients</a>, signature (0,0,0,3,0,0,0,-3,0,0,0,1).
%F A347650 a(n) = (n+3)/2   for n = 3 (mod 4)
%F A347650      = 2         for n = 0 (mod 4)
%F A347650      = (n+1)/2   for n = 1 (mod 3)
%F A347650      = (n+2)^2/8 for n = 2 (mod 4).
%F A347650 a(n) = 3*a(n-4)-3*a(n-8)+a(n-12) for n > 12.
%F A347650 G.f.: x*(-1-2*x-3*x^2-2*x^3-2*x^5+4*x^6+4*x^7+x^8-x^10-2*x^11)/(-1+x^4)^3.
%t A347650 Table[Piecewise[{{(n + 3)/2, Mod[n, 4] == 3}, {2, Mod[n, 4] == 0}, {(n + 1)/2, Mod[n, 4] == 1}, {(n + 2)^2/8, Mod[n, 4] == 2}}], {n, 20}]
%t A347650 LinearRecurrence[{0, 0, 0, 3, 0, 0, 0, -3, 0, 0, 0, 1}, {1, 2, 3, 2, 3, 8, 5, 2, 5, 18, 7, 2}, 20]
%t A347650 CoefficientList[Series[(-1 - 2 x - 3 x^2 - 2 x^3 - 2 x^5 + 4 x^6 + 4 x^7 + x^8 - x^10 - 2 x^11)/(-1 + x^4)^3, {x, 0, 20}], x]
%Y A347650 Cf. A004524, A302506, A303148.
%K A347650 nonn
%O A347650 1,2
%A A347650 _Eric W. Weisstein_, Sep 09 2021