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 A290589 #27 Sep 04 2025 15:34:45
%S A290589 41,113,320,908,2574,7317,20855,59582,170681,490180,1411207,4072092,
%T A290589 11774998,34114389,99006951,287783255,837649471,2441108294,7121588680,
%U A290589 20795782761,60775937523,177746557324,520168686310,1523090681155,4461852378404,13076323061624
%N A290589 Number of irredundant sets in the n-gear graph.
%H A290589 Christian Sievers, <a href="/A290589/b290589.txt">Table of n, a(n) for n = 3..200</a>
%H A290589 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/GearGraph.html">Gear Graph</a>.
%H A290589 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/IrredundantSet.html">Irredundant Set</a>.
%H A290589 <a href="/index/Rec#order_17">Index entries for linear recurrences with constant coefficients</a>, signature (11,-45,74,1,-140,100,58,-49,19,-57,-4,40,-2,-7,-11,0,4).
%F A290589 a(n) = 11*a(n-1)-45*a(n-2)+74*a(n-3)+a(n-4)-140*a(n-5)+100*a(n-6)+58*a(n-7)-49*a(n-8)+19*a(n-9)-57*a(n-10)-4*a(n-11)+40*a(n-12)-2*a(n-13)-7*a(n-14)-11*a(n-15)+4*a(n-17) for n > 20. - _Eric W. Weisstein_, Sep 04 2025
%F A290589 G.f.: x^3*(-41+338*x-922*x^2+561*x^3+1417*x^4-1810*x^5-406*x^6+820*x^7-297*x^8+950*x^9-135*x^10-664*x^11+180*x^12+172*x^13+154*x^14-37*x^15-70*x^16+6*x^17)/((-1+2*x)^2*(-1+x+x^2)*(-1+2*x+x^2+x^3)*(-1+x+x^2+x^3+x^4)*(1-3*x-x^2+4*x^3-x^4-2*x^5+x^6)). - _Eric W. Weisstein_, Sep 04 2025
%t A290589 Join[{41}, Table[2^(n - 4) n + LucasL[n] + RootSum[-1 - # - 2 #^2 + #^3 &, #^n &] - RootSum[-1 - # - #^2 - #^3 + #^4 &, #^n &] + RootSum[1 - 2 # - #^2 + 4 #^3 - #^4 - 3 #^5 + #^6 &, #^n &], {n, 4, 10}]] (* _Eric W. Weisstein_, Sep 04 2025 *)
%t A290589 Join[{41}, LinearRecurrence[{11, -45, 74, 1, -140, 100, 58, -49, 19, -57, -4, 40, -2, -7, -11, 0, 4}, {113, 320, 908, 2574, 7317, 20855, 59582, 170681, 490180, 1411207, 4072092, 11774998, 34114389, 99006951, 287783255, 837649471, 2441108294}, 20]] (* _Eric W. Weisstein_, Sep 04 2025 *)
%t A290589 CoefficientList[Series[(-41 + 338 x - 922 x^2 + 561 x^3 + 1417 x^4 - 1810 x^5 - 406 x^6 + 820 x^7 - 297 x^8 + 950 x^9 - 135 x^10 - 664 x^11 + 180 x^12 + 172 x^13 + 154 x^14 - 37 x^15 - 70 x^16 + 6 x^17)/((-1 + 2 x)^2 (-1 + x + x^2) (-1 + 2 x + x^2 + x^3) (-1 + x + x^2 + x^3 + x^4) (1 - 3 x - x^2 + 4 x^3 - x^4 - 2 x^5 + x^6)), {x, 0, 20}], x] (* _Eric W. Weisstein_, Sep 04 2025 *)
%Y A290589 Cf. A290378, A290640.
%K A290589 nonn,changed
%O A290589 3,1
%A A290589 _Eric W. Weisstein_, Aug 07 2017
%E A290589 a(13)-a(16) from _Andrew Howroyd_, Aug 11 2017
%E A290589 Missing a(12) inserted and a(17)-a(18) added by _Andrew Howroyd_, Aug 27 2017
%E A290589 More terms from _Christian Sievers_, Nov 18 2023