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 A290378 #26 Feb 16 2025 08:33:49
%S A290378 2,8,8,16,37,80,156,304,602,1173,2290,4456,8686,16892,32833,63776,
%T A290378 123864,240524,467060,907061,1761894,3423164,6652706,12933280,
%U A290378 25151787,48931280,95228360,185400336,361093444,703546005,1371282460,2673742784,5215147858
%N A290378 Number of minimal dominating sets in the n-gear graph.
%C A290378 Sequence extrapolated to n = 1 using recurrence. - _Andrew Howroyd_, Aug 27 2017
%H A290378 Andrew Howroyd, <a href="/A290378/b290378.txt">Table of n, a(n) for n = 1..200</a>
%H A290378 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/GearGraph.html">Gear Graph</a>
%H A290378 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/MinimalDominatingSet.html">Minimal Dominating Set</a>
%H A290378 <a href="/index/Rec#order_13">Index entries for linear recurrences with constant coefficients</a>, signature (4, -3, -4, 4, -1, 1, 3, -3, 0, 2, 3, 0, -1).
%F A290378 From _Andrew Howroyd_, Aug 27 2017: (Start)
%F A290378 a(n) = 4*a(n-1) - 3*a(n-2) - 4*a(n-3) + 4*a(n-4) - a(n-5) + a(n-6) + 3*a(n-7) - 3*a(n-8) + 2*a(n-10) + 3*a(n-11) - a(n-13) for n > 13.
%F A290378 G.f.: x*(2 - 18*x^2 + 16*x^3 + 21*x^4 - 18*x^5 - 15*x^6 - 2*x^7 + 16*x^8 + 2*x^9 + 11*x^10 - 2*x^11 - 5*x^12)/((1 + x^2)*(1 - x - x^2)*(1 - x - x^2 - x^3)*(1 - 2*x - x^2 + 3*x^3 - x^4 - 2*x^5 + x^6)).
%F A290378 (End)
%t A290378 Table[RootSum[-1 - # - #^2 + #^3 &, #^n &] + RootSum[1 - 2 # - #^2 + 3 #^3 - #^4 - 2 #^5 + #^6 &, #^n &] - LucasL[n] - 2 Cos[n Pi/2], {n, 20}]
%t A290378 LinearRecurrence[{4, -3, -4, 4, -1, 1, 3, -3, 0, 2, 3, 0, -1}, {2, 8, 8, 16, 37, 80, 156, 304, 602, 1173, 2290, 4456, 8686}, 20]
%t A290378 CoefficientList[Series[(2 - 18 x^2 + 16 x^3 + 21 x^4 - 18 x^5 - 15 x^6 - 2 x^7 + 16 x^8 + 2 x^9 + 11 x^10 - 2 x^11 - 5 x^12)/((1 + x^2) (1 - x - x^2) (1 - x - x^2 - x^3) (1 - 2 x - x^2 + 3 x^3 - x^4 - 2 x^5 + x^6)), {x, 0, 20}], x]
%o A290378 (PARI) Vec((2 - 18*x^2 + 16*x^3 + 21*x^4 - 18*x^5 - 15*x^6 - 2*x^7 + 16*x^8 + 2*x^9 + 11*x^10 - 2*x^11 - 5*x^12)/((1 + x^2)*(1 - x - x^2)*(1 - x - x^2 - x^3)*(1 - 2*x - x^2 + 3*x^3 - x^4 - 2*x^5 + x^6)) + O(x^30)) \\ _Andrew Howroyd_, Aug 27 2017
%Y A290378 Cf. A290589, A290938.
%K A290378 nonn
%O A290378 1,1
%A A290378 _Eric W. Weisstein_, Jul 28 2017
%E A290378 a(13)-a(24) from _Andrew Howroyd_, Aug 11 2017
%E A290378 a(1)-a(2) and terms a(25) and beyond from _Andrew Howroyd_, Aug 27 2017