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 A227712 #34 Sep 08 2022 08:46:05
%S A227712 4,10,25,58,127,268,553,1126,2275,4576,9181,18394,36823,73684,147409,
%T A227712 294862,589771,1179592,2359237,4718530,9437119,18874300,37748665,
%U A227712 75497398,150994867,301989808,603979693,1207959466,2415919015,4831838116,9663676321,19327352734
%N A227712 a(n) = 9*2^n - 3*n - 5.
%C A227712 Denoting by P[n] the path on n vertices, a(n) is the number of vertices of the tree obtained by identifying the roots of 3 identical rooted trees g[n], where g[n] is obtained recursively in the following manner: g[0]=P[2] and g[n] (n>=1) is obtained by identifying the roots of 2 copies of g[n-1] and one of the extremities of P[n+1]; the root of g[n] is defined to be the other extremity of P[n+1]. Most references contain pictures of these trees; however, the small circles have to be viewed as vertices rather than hexagons.
%H A227712 R. Kopelman, M. Shortreed, Z. Y. Shi, W. Tan, Z. F. Xu, J. S. Moore, A. Bar-Haim, J. Klafter, <a href="http://dx.doi.org/10.1103/PhysRevLett.78.1239">Spectroscopic evidence for excitonic localization in fractal antenna supermolecules</a>, Phys. Rev. Letters, 78, 1997, 1239-1242.
%H A227712 M. A. MartÃn-Delgado, J. Rodriguez-Laguna, G. Sierra, <a href="http://dx.doi.org/10.1103/PhysRevB.65.155116">A density matrix renormalization group study of excitons in dendrimers</a>, Phys. Rev. B 65, 2002, 155116(1-11).
%H A227712 S. Raychaudhuri, Y. Shapir, S. Mukamel, <a href="http://dx.doi.org/10.1103/PhysRevE.65.021803">Disorder and funneling effect on exciton migration in treelike dendrimers</a>, Phys. Rev. E, 65, 2002, 021803(1-12).
%H A227712 S. Tretiak, V. Chernyak, S. Mukamel, <a href="http://mukamel.ps.uci.edu/publications/pdfs/367.pdf">Localized electronic excitations in phenylacetylene dendrimers</a>, J. Phys. Chem. B, 102, 1998, 3310-3315.
%H A227712 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (4,-5,2).
%F A227712 G.f.: (4-6*x+5*x^2)/((1-2*x)*(1-x)^2).
%F A227712 a(0)=4, a(1)=10, a(2)=25, a(n) = 4*a(n-1)-5*a(n-2)+2*a(n-3). - _Harvey P. Dale_, Apr 15 2015
%F A227712 a(n)= 3*A079583(n) + 1. - _Emeric Deutsch_, Feb 18 2016
%e A227712 a(1) = 10 because g[1] is the rooted tree in the shape of Y (4 vertices) and a "bouquet" of three Y's has 3*4 - 2 = 10 vertices.
%p A227712 a := proc (n) options operator, arrow: 9*2^n-3*n-5 end proc: seq(a(n), n = 0 .. 35);
%t A227712 Table[9*2^n-3n-5,{n,0,40}] (* or *) LinearRecurrence[{4,-5,2},{4,10,25},40] (* _Harvey P. Dale_, Apr 15 2015 *)
%o A227712 (PARI) Vec((4-6*x+5*x^2)/((1-2*x)*(1-x)^2) + O(x^100)) \\ _Altug Alkan_, Oct 17 2015
%o A227712 (Magma) [9*2^n-3*n-5: n in [0..40]]; // _Vincenzo Librandi_, Feb 19 2016
%Y A227712 Cf. A079583.
%K A227712 nonn,easy
%O A227712 0,1
%A A227712 _Emeric Deutsch_, Aug 06 2013