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 A092807 #41 Jan 31 2024 10:56:10
%S A092807 1,2,8,40,224,1312,7808,46720,280064,1679872,10078208,60467200,
%T A092807 362799104,2176786432,13060702208,78364180480,470185017344,
%U A092807 2821109972992,16926659575808,101559956930560,609359740534784
%N A092807 Expansion of (1-6*x+4*x^2)/((1-2*x)*(1-6*x)).
%C A092807 Second binomial transform of A054881 (closed walks at a vertex of an octahedron) With interpolated zeros, counts closed walks of length n at a vertex of the edge-vertex incidence graph of K_4 associated with the edges of K_4.
%C A092807 This also gives the number of noncrossing, nonnesting, 2-colored permutations on {1, 2, ..., n}. - _Lily Yen_, Apr 22 2013
%H A092807 G. C. Greubel, <a href="/A092807/b092807.txt">Table of n, a(n) for n = 0..1000</a>
%H A092807 Lily Yen, <a href="http://arxiv.org/abs/1211.3472">Crossings and Nestings for Arc-Coloured Permutations</a>, arXiv:1211.3472 [math.CO], 2012-2013 and <a href="https://doi.org/10.46298/dmtcs.2339">Arc-coloured permutations</a>, PSAC 2013, Paris, France, June 24-28, Proc. DMTCS (2013) 743-754.
%H A092807 Lily Yen, <a href="https://doi.org/10.37236/4080">Crossings and Nestings for Arc-Coloured Permutations and Automation</a>, Electronic Journal of Combinatorics, 22(1) (2015), #P1.14.
%H A092807 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (8,-12).
%F A092807 G.f.: (1-6*x+4*x^2)/((1-2*x)*(1-6*x)).
%F A092807 a(n) = (6^n + 3*2^n + 2*0^n)/6.
%F A092807 a(n) = A074601(n-1), n>0. - _R. J. Mathar_, Sep 08 2008
%F A092807 a(0)=1, a(1)=2, a(2)=8, a(n) = 8*a(n-1)-12*a(n-2). - _Harvey P. Dale_, Aug 23 2011
%F A092807 a(n) = A124302(n)*2^n. - _Philippe Deléham_, Nov 01 2011
%F A092807 E.g.f.: (1/6)*( 1 + 3*exp(2*x) + exp(6*x) ). - _G. C. Greubel_, Jan 04 2023
%t A092807 CoefficientList[Series[(1-6x+4x^2)/((1-2x)(1-6x)),{x,0,40}],x] (* or *) LinearRecurrence[{8,-12},{1,2,8},41] (* _Harvey P. Dale_, Aug 23 2011 *)
%o A092807 (Magma) [1] cat [6^(n-1) + 2^(n-1): n in [1..40]]; // _G. C. Greubel_, Jan 04 2023
%o A092807 (SageMath) [(6^n + 3*2^n + 2*0^n)/6 for n in range(41)] # _G. C. Greubel_, Jan 04 2023
%Y A092807 Cf. A054881, A074601, A092803, A124302.
%K A092807 easy,nonn
%O A092807 0,2
%A A092807 _Paul Barry_, Mar 06 2004