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 A302402 #13 Feb 16 2025 08:33:53
%S A302402 0,2,2,2,4,4,4,6,6,6,8,8,8,10,10,10,12,12,12,14,14,14,16,16,16,18,18,
%T A302402 18,20,20,20,22,22,22,24,24,24,26,26,26,28,28,28,30,30,30,32,32,32,34,
%U A302402 34,34,36,36,36,38,38,38,40,40,40,42,42,42,44,44,44,46,46,46,48
%N A302402 Total domination number of the n-ladder graph.
%C A302402 Extended to a(0) using the formula/recurrence.
%H A302402 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/LadderGraph.html">Ladder Graph</a>
%H A302402 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/TotalDominationNumber.html">Total Domination Number</a>
%H A302402 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (1, 0, 1, -1).
%F A302402 a(n) = 2*floor((n + 2)/3).
%F A302402 a(n) = 2/9*(3 + 3*n - 3*cos(2*n*Pi/3) + sqrt(3)*sin(2*n*Pi/3)).
%F A302402 a(n) = a(n-1) + a(n-3) - a(n-4).
%F A302402 G.f.: 2*x/((-1 + x)^2*(1 + x + x^2)).
%F A302402 a(n) = 2*A002264(n+2). - _R. J. Mathar_, May 02 2023
%t A302402 Table[2 Floor[(n + 2)/3], {n, 0, 20}]
%t A302402 2 Floor[(Range[0, 20] + 2)/3]
%t A302402 Table[2/9 (3 + 3 n - 3 Cos[2 n Pi/3] + Sqrt[3] Sin[2 n Pi/3]), {n, 0, 20}]
%t A302402 LinearRecurrence[{1, 0, 1, -1}, {2, 2, 2, 4}, {0, 20}]
%t A302402 CoefficientList[Series[2 x/((-1 + x)^2 (1 + x + x^2)), {x, 0, 20}], x]
%K A302402 nonn,easy
%O A302402 0,2
%A A302402 _Eric W. Weisstein_, Apr 07 2018