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 A295420 #24 Feb 16 2025 08:33:52
%S A295420 1,11,49,131,441,1499,5041,17155,58081,196331,664225,2246915,7601049,
%T A295420 25714875,86992929,294294531,995591809,3368061131,11394068049,
%U A295420 38545859971,130399709881,441139059867,1492362754129,5048627019523,17079382863841,57779138374059
%N A295420 Number of total dominating sets in the n-Moebius ladder.
%C A295420 Sequence extrapolated to n=1 using recurrence. - _Andrew Howroyd_, Apr 16 2018
%H A295420 Andrew Howroyd, <a href="/A295420/b295420.txt">Table of n, a(n) for n = 1..200</a>
%H A295420 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/MoebiusLadder.html">Moebius Ladder</a>
%H A295420 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/TotalDominatingSet.html">Total Dominating Set</a>
%H A295420 <a href="/index/Rec#order_09">Index entries for linear recurrences with constant coefficients</a>, signature (3,0,4,-2,10,4,0,-1,-1).
%F A295420 From _Andrew Howroyd_, Apr 16 2018: (Start)
%F A295420 G.f.: x*(1 - x)*(1 + 9*x + 25*x^2 + 5*x^3 + 11*x^4 + 3*x^5 + 7*x^6 + 3*x^7)/((1 - x + x^2 + x^3)*(1 + x + x^2 - x^3)*(1 - 3*x - x^2 - x^3)).
%F A295420 a(n) = 3*a(n-1) + 4*a(n-3) - 2*a(n-4) + 10*a(n-5) + 4*a(n-6) - a(n-8) - a(n-9) for n > 9. (End)
%t A295420 Table[RootSum[-1 - # - 3 #^2 + #^3 &, #^n &] - RootSum[1 + # - #^2 + #^3 &, #^n &] + RootSum[-1 + # + #^2 + #^3 &, #^n &], {n, 20}]
%t A295420 LinearRecurrence[{3, 0, 4, -2, 10, 4, 0, -1, -1}, {1, 11, 49, 131, 441, 1499, 5041, 17155, 58081}, 20]
%t A295420 CoefficientList[Series[(1 + 8 x + 16 x^2 - 20 x^3 + 6 x^4 - 8 x^5 + 4 x^6 - 4 x^7 - 3 x^8)/(1 - 3 x - 4 x^3 + 2 x^4 - 10 x^5 - 4 x^6 + x^8 + x^9), {x, 0, 20}], x]
%o A295420 (PARI) Vec((1 - x)*(1 + 9*x + 25*x^2 + 5*x^3 + 11*x^4 + 3*x^5 + 7*x^6 + 3*x^7)/((1 - x + x^2 + x^3)*(1 + x + x^2 - x^3)*(1 - 3*x - x^2 - x^3)) + O(x^30)) \\ _Andrew Howroyd_, Apr 16 2018
%Y A295420 Cf. A284663, A290337.
%K A295420 nonn,easy
%O A295420 1,2
%A A295420 _Eric W. Weisstein_, Apr 16 2018
%E A295420 a(1)-a(2) and terms a(10) and beyond from _Andrew Howroyd_, Apr 16 2018