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 A372027 #15 Jan 22 2025 05:59:29
%S A372027 12,33,61,96,135,181,233,291,355,425,501,583,671,765,865,971,1083,
%T A372027 1201,1325,1455,1591,1733,1881,2035,2195,2361,2533,2711,2895,3085,
%U A372027 3281,3483,3691,3905,4125,4351,4583,4821,5065,5315,5571,5833,6101,6375,6655,6941,7233,7531
%N A372027 Maximum second Zagreb index of maximal outerplanar graphs with n vertices.
%C A372027 The second Zagreb index of a graph is the sum of the products of the degrees over all edges of the graph.
%C A372027 A maximal outerplanar graph has all vertices on the exterior region, and all other regions triangles. The extremal graphs are fans, except when n=6. Then the extremal graph is the triangular grid with degrees 4,4,4,2,2,2.
%H A372027 Paolo Xausa, <a href="/A372027/b372027.txt">Table of n, a(n) for n = 3..10000</a>
%H A372027 Allan Bickle, <a href="https://doi.org/10.20429/tag.2024.000105">A Survey of Maximal k-degenerate Graphs and k-Trees</a>, Theory and Applications of Graphs 0 1 (2024) Article 5.
%H A372027 Allan Bickle, <a href="https://ajc.maths.uq.edu.au/pdf/89/ajc_v89_p167.pdf">Zagreb Indices of Maximal k-degenerate Graphs</a>, Australas. J. Combin. 89 1 (2024) 167-178.
%H A372027 J. Estes and B. Wei, <a href="https://doi.org/10.1007/s10878-012-9515-6">Sharp bounds of the Zagreb indices of k-trees</a>, J Comb Optim 27 (2014), 271-291.
%H A372027 A. Hou, S. Li, L. Song, and B. Wei, <a href="https://doi.org/10.1007/s10878-010-9288-8">Sharp bounds for Zagreb indices of maximal outerplanar graphs</a>, J Comb Optim 22 (2011), 252-269.
%H A372027 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (3,-3,1).
%F A372027 a(n) = 3*n^2 + n - 19 when n is not 3 or 6.
%F A372027 From _Chai Wah Wu_, Apr 16 2024: (Start)
%F A372027 a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) for n > 9.
%F A372027 G.f.: x^3*(x^6 - 3*x^5 + 3*x^4 + 2*x^2 + 3*x - 12)/(x - 1)^3. (End)
%e A372027 The graph K_3 has 3 degree 2 vertices, so a(3) = 3*4 = 12.
%t A372027 LinearRecurrence[{3, -3, 1}, {12, 33, 61, 96, 135, 181, 233}, 50] (* _Paolo Xausa_, Jan 22 2025 *)
%Y A372027 Cf. A002378, A152811, A371912 (Zagreb indices of maximal k-degenerate graphs).
%Y A372027 Cf. A051624, A372025, A372026 (second Zagreb indices of maximal k-degenerate graphs).
%K A372027 nonn
%O A372027 3,1
%A A372027 _Allan Bickle_, Apr 16 2024