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 A303834 #11 Feb 16 2025 08:33:54
%S A303834 3,21,48,161,473,1476,4553,14241,44688,141081,447153,1422596,4539473,
%T A303834 14522361,46556048,149508801,480810153,1548053316,4988972313,
%U A303834 16090635281,51928966928,167675418921,541639730273,1750245266436,5657268819873,18289912673001
%N A303834 Number of total dominating sets in the n-gear graph.
%C A303834 Extended to a(1)-a(2) using the formula/recurrence.
%H A303834 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/GearGraph.html">Gear Graph</a>
%H A303834 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/TotalDominatingSet.html">Total Dominating Set</a>
%H A303834 <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (4,2,-13,-6,4).
%F A303834 a(n) = 2*(-1)^n + 2^n*A000032(n) + A005248(n).
%F A303834 a(n) = 4*a(n-1) + 2*a(n-2) - 13*a(n-3) - 6*a(n-4) + 4*a(n-5).
%F A303834 G.f.: -x*(3+9*x-42*x^2-34*x^3+24*x^4) / ( (1+x)*(x^2-3*x+1)*(4*x^2+2*x-1) ).
%t A303834 Table[2 (-1)^n + 2^n LucasL[n] + LucasL[2 n], {n, 20}]
%t A303834 LinearRecurrence[{4, 2, -13, -6, 4}, {3, 21, 48, 161, 473}, 20]
%t A303834 CoefficientList[Series[(-3 - 9 x + 42 x^2 + 34 x^3 - 24 x^4)/(-1 + 4 x + 2 x^2 - 13 x^3 - 6 x^4 + 4 x^5), {x, 0, 20}], x]
%K A303834 nonn,easy
%O A303834 1,1
%A A303834 _Eric W. Weisstein_, May 02 2018