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 A020877 #52 Feb 16 2025 08:32:34
%S A020877 10,34,106,344,1102,3546,11394,36628,117730,378426,1216378,3909832,
%T A020877 12567446,40395794,129844994,417363332,1341539194,4312135922,
%U A020877 13860583626,44552347608,143205490526,460308235562,1479577849602,4755836293844,15286778495570,49136593930954
%N A020877 Number of matchings in Moebius ladder M_n.
%C A020877 Also the Hosoya indices of the Moebius ladders. - _Eric W. Weisstein_, Jul 11 2011
%H A020877 Colin Barker, <a href="/A020877/b020877.txt">Table of n, a(n) for n = 2..1000</a>
%H A020877 J. P. McSorley, <a href="http://dx.doi.org/10.1016/S0012-365X(97)00086-1">Counting structures in the Moebius ladder</a>, Discrete Math., 184 (1998), 137-164.
%H A020877 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/IndependentEdgeSet.html">Independent Edge Set</a>
%H A020877 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/Matching.html">Matching</a>
%H A020877 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/MoebiusLadder.html">Moebius Ladder</a>
%H A020877 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (2,4,0,-1).
%F A020877 G.f.: 2*x^2*(5+7*x-x^2-2*x^3)/((1+x)*(1-3*x-x^2+x^3)). - _Emeric Deutsch_, Dec 21 2004
%F A020877 a(n) = 2*a(n-1) + 4*a(n-2) - a(n-4). - _Eric W. Weisstein_, Oct 03 2017 [Corrected by _Altug Alkan_, Apr 06 2018]
%F A020877 The McSorley reference gives the approximation a(n)~(3.2143)^n+(-0.6751)^n+(0.4608)^n-(-1)^n. - _Emeric Deutsch_, Dec 21 2004
%p A020877 G:=2*x^2*(5+7*x-x^2-2*x^3)/(1+x)/(1-3*x-x^2+x^3): Gser:=series(G,x=0,29): seq(coeff(Gser,x^n),n=2..27); # _Emeric Deutsch_, Dec 21 2004
%t A020877 Table[RootSum[1 - # - 3 #^2 + #^3 &, #^n &] - (-1)^n, {n, 2, 20}] (* _Eric W. Weisstein_, Mar 31 2017 *)
%t A020877 LinearRecurrence[{2, 4, 0, -1}, {10, 34, 106, 344}, 20] (* _Eric W. Weisstein_, Mar 31 2017 *)
%t A020877 CoefficientList[Series[-2 (-5 - 7 x + x^2 + 2 x^3)/(1 - 2 x - 4 x^2 + x^4), {x, 0, 20}], x] (* _Eric W. Weisstein_, Oct 03 2017 *)
%o A020877 (PARI) Vec(-2*x^2*(2*x^3+x^2-7*x-5)/((x+1)*(x^3-x^2-3*x+1)) + O(x^50)) \\ _Colin Barker_, Aug 01 2015
%o A020877 (Magma) I:=[10,34,106,344]; [n le 4 select I[n] else 2*Self(n-1)+4*Self(n-2)-Self(n-4): n in [1..30]]; // _Vincenzo Librandi_, Apr 07 2018
%Y A020877 Row sums of A302232.
%K A020877 nonn,easy
%O A020877 2,1
%A A020877 _N. J. A. Sloane_
%E A020877 More terms from _Emeric Deutsch_, Dec 21 2004