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 A364741 #22 Feb 16 2025 08:34:06
%S A364741 0,8,160,2009,25872,328208,4165357,52837520,670238112,8501756249,
%T A364741 107841947320,1367938389320,17351831692125,220102059219128,
%U A364741 2791919445762040,35414544563765129,449221401563485632,5698220042111151488,72279974941308391117,916846794068851162400,11629888423130623254672
%N A364741 Number of edge covers in the n-double cone graph.
%C A364741 The n-double cone graph is defined for n >= 3. The sequence has been extended to a(0)-a(2) using the formula/recurrence. - _Andrew Howroyd_, Aug 08 2023
%H A364741 Andrew Howroyd, <a href="/A364741/b364741.txt">Table of n, a(n) for n = 0..200</a>
%H A364741 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/DoubleConeGraph.html">Double Cone Graph</a>
%H A364741 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/EdgeCover.html">Edge Cover</a>
%H A364741 <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (13,2,-75,-17,38,-8).
%F A364741 From _Andrew Howroyd_, Aug 08 2023: (Start)
%F A364741 a(n) = A206776(n)^2 - A000032(n)^2.
%F A364741 a(n) = 13*a(n-1) + 2*a(n-2) - 75*a(n-3) - 17*a(n-4) + 38*a(n-5) - 8*a(n-6) for n >= 6.
%F A364741 G.f.: x*(8 + 56*x - 87*x^2 + 35*x^3 - 10*x^4)/((1 + x)*(1 + 2*x)*(1 - 3*x + x^2)*(1 - 13*x + 4*x^2)). (End)
%t A364741 LinearRecurrence[{13, 2, -75, -17, 38, -8}, {0, 8, 160, 2009, 25872, 328208}, 25] (* _Paolo Xausa_, Nov 18 2023 *)
%t A364741 CoefficientList[Series[-x (-8 - 56 x + 87 x^2 - 35 x^3 + 10 x^4)/((1 + x) (1 + 2 x) (1 - 3 x + x^2) (1 - 13 x + 4 x^2)), {x, 0, 20}], x] (* _Eric W. Weisstein_, May 25 2024 *)
%t A364741 Table[2 (-1)^n (2^n - 1) - LucasL[2 n] + ((13 - 3 Sqrt[17])^n + (13 + 3 Sqrt[17])^n)/2^n, {n, 20}] // Expand (* _Eric W. Weisstein_, May 25 2024 *)
%o A364741 (PARI) concat(0, Vec((8 + 56*x - 87*x^2 + 35*x^3 - 10*x^4)/((1 + x)*(1 + 2*x)*(1 - 3*x + x^2)*(1 - 13*x + 4*x^2)) + O(x^20))) \\ _Andrew Howroyd_, Aug 08 2023
%Y A364741 Cf. A000032, A206776, A297047.
%K A364741 nonn,easy
%O A364741 0,2
%A A364741 _Eric W. Weisstein_, Aug 05 2023
%E A364741 a(0)-a(2) and terms a(8) and beyond from _Andrew Howroyd_, Aug 08 2023