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 A290698 #15 Feb 16 2025 08:33:50
%S A290698 2,14,74,286,1157,4778,19623,80478,330293,1355629,5563527,22832914,
%T A290698 93707772,384582275,1578347684,6477630782,26584574434,109104640685,
%U A290698 447771795953,1837681518261,7541951930181,30952609765223,127031312347552,521343900861138
%N A290698 Number of minimal edge covers in the n-antiprism graph.
%C A290698 The n-antiprism graph is well defined for n >= 3. Sequence extended to n = 1 using recurrence. - _Andrew Howroyd_, Aug 10 2017
%H A290698 Andrew Howroyd, <a href="/A290698/b290698.txt">Table of n, a(n) for n = 1..200</a>
%H A290698 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/AntiprismGraph.html">Antiprism Graph</a>
%H A290698 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/MinimalEdgeCover.html">Minimal Edge Cover</a>
%H A290698 <a href="/index/Rec#order_09">Index entries for linear recurrences with constant coefficients</a>, signature (2, 5, 12, 11, 5, -3, -4, -1, 1).
%F A290698 From _Andrew Howroyd_, Aug 10 2017: (Start)
%F A290698 a(n) = 2*a(n-1) + 5*a(n-2) + 12*a(n-3) + 11*a(n-4) + 5*a(n-5) - 3*a(n-6) - 4*a(n-7) - a(n-8) + a(n-9).
%F A290698 G.f.: x*(2 + 10*x + 36*x^2 + 44*x^3 + 25*x^4 - 18*x^5 - 28*x^6 - 8*x^7 + 9*x^8)/((1 - 3*x - 3*x^2 - 6*x^3 - 2*x^4 + 3*x^5 + 2*x^6 - x^7)*(1 + x + x^2)).
%F A290698 (End)
%t A290698 Table[2 Cos[2 n Pi/3] + RootSum[-1 + 2 # + 3 #^2 - 2 #^3 - 6 #^4 - 3 #^5 - 3 #^6 + #^7 &, #^n &], {n, 20}]
%t A290698 LinearRecurrence[{2, 5, 12, 11, 5, -3, -4, -1, 1}, {2, 14, 74, 286, 1157, 4778, 19623, 80478, 330293}, 20]
%t A290698 CoefficientList[Series[(-2 - 10 x - 36 x^2 - 44 x^3 - 25 x^4 + 18 x^5 + 28 x^6 + 8 x^7 - 9 x^8)/(-1 + 2 x + 5 x^2 + 12 x^3 + 11 x^4 + 5 x^5 - 3 x^6 - 4 x^7 - x^8 + x^9), {x, 0, 20}], x]
%o A290698 (PARI)
%o A290698 Vec((2 + 10*x + 36*x^2 + 44*x^3 + 25*x^4 - 18*x^5 - 28*x^6 - 8*x^7 + 9*x^8)/((1 - 3*x - 3*x^2 - 6*x^3 - 2*x^4 + 3*x^5 + 2*x^6 - x^7)*(1 + x + x^2)) + O(x^30)) \\ _Andrew Howroyd_, Aug 10 2017
%Y A290698 Cf. A284700.
%K A290698 nonn
%O A290698 1,1
%A A290698 _Eric W. Weisstein_, Aug 09 2017
%E A290698 a(1)-a(2) and terms a(7) and beyond from _Andrew Howroyd_, Aug 10 2017