This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A302404 #22 Feb 16 2025 08:33:53
%S A302404 0,2,2,2,3,4,4,6,6,6,7,8,8,10,10,10,11,12,12,14,14,14,15,16,16,18,18,
%T A302404 18,19,20,20,22,22,22,23,24,24,26,26,26,27,28,28,30,30,30,31,32,32,34,
%U A302404 34,34,35,36,36,38,38,38,39,40,40,42,42,42,43,44,44,46,46,46,47
%N A302404 Total domination number of the n-Moebius ladder.
%C A302404 Extended to a(0)-a(2) using the formula/recurrence.
%H A302404 G. C. Greubel, <a href="/A302404/b302404.txt">Table of n, a(n) for n = 0..10000</a>
%H A302404 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/MoebiusLadder.html">Moebius Ladder</a>
%H A302404 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/TotalDominationNumber.html">Total Domination Number</a>
%H A302404 <a href="/index/Rec#order_07">Index entries for linear recurrences with constant coefficients</a>, signature (1,0,0,0,0,1,-1).
%F A302404 a(n) = (3 - (-1)^n + 4*n + cos(n*Pi/3) - 3*cos(2*n*Pi/3) + sqrt(3)*sin(n*Pi/3) + sin(2*n*Pi/3)/sqrt(3))/6.
%F A302404 a(n) = a(n-1) + a(n-6) - a(n-7).
%F A302404 G.f.: x*(2 + x^3 + x^4)/((1 - x)^2*(1 + x + x^2 + x^3 + x^4 + x^5)).
%F A302404 a(n) = a(n-6) + 4. - _Andrew Howroyd_, Apr 18 2018
%F A302404 a(n) = a(n-6*k) + 4*k. - _Eric W. Weisstein_, Apr 23 2018
%t A302404 Table[(3 - (-1)^n + 4 n + Cos[n Pi/3] - 3 Cos[2 n Pi/3] + Sqrt[3] Sin[n Pi/3] + Sin[2 n Pi/3]/Sqrt[3])/6, {n, 0, 20}]
%t A302404 LinearRecurrence[{1,0,0,0,0,1,-1}, {2,2,2,3,4,4,6}, {0, 50}]
%t A302404 CoefficientList[Series[x (2 + x^3 + x^4)/((-1 + x)^2 (1 + x + x^2 + x^3 + x^4 + x^5)), {x, 0, 20}], x]
%o A302404 (PARI) x='x+O('x^50); concat(0, Vec(x*(2+x^3+x^4)/((1-x)^2*(1+x+x^2+x^3+x^4+x^5)))) \\ _G. C. Greubel_, Apr 09 2018
%o A302404 (Magma) I:=[2,2,2,3,4,4,6]; [0] cat [n le 7 select I[n] else Self(n-1) + Self(n-6) - Self(n-7): n in [1..50]]; // _G. C. Greubel_, Apr 09 2018
%Y A302404 Cf. A295420, A302405, A303046, A301337.
%K A302404 nonn,easy
%O A302404 0,2
%A A302404 _Eric W. Weisstein_, Apr 07 2018