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 A372026 #13 Jan 22 2025 05:28:59
%S A372026 12,33,51,86,116,147,178,210,242,274,306,338,370,402,434,466,498,530,
%T A372026 562,594,626,658,690,722,754,786,818,850,882,914,946,978,1010,1042,
%U A372026 1074,1106,1138,1170,1202,1234,1266,1298,1330,1362,1394,1426,1458,1490,1522,1554,1586,1618,1650,1682,1714,1746,1778,1810
%N A372026 Minimum second Zagreb index of maximal 2-degenerate graphs with n vertices.
%C A372026 The second Zagreb index of a graph is the sum of the products of the degrees over all edges of the graph.
%C A372026 A maximal 2-degenerate graph can be constructed from a 2-clique by iteratively adding a new 2-leaf (vertex of degree 2) adjacent to two existing vertices. The extremal graphs are described in (Bickle 2024).
%H A372026 Paolo Xausa, <a href="/A372026/b372026.txt">Table of n, a(n) for n = 3..10000</a>
%H A372026 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 A372026 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 A372026 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 A372026 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (2,-1).
%F A372026 a(n) = 32*n-110 for n>8.
%F A372026 From _Chai Wah Wu_, Apr 16 2024: (Start)
%F A372026 a(n) = 2*a(n-1) - a(n-2) for n > 10.
%F A372026 G.f.: x^3*(x^7 + x^5 - 5*x^4 + 17*x^3 - 3*x^2 + 9*x + 12)/(x - 1)^2. (End)
%e A372026 The graph K_3 has 3 degree 2 vertices, so a(3) = 3*4 = 12.
%t A372026 LinearRecurrence[{2, -1}, {12, 33, 51, 86, 116, 147, 178, 210}, 60] (* _Paolo Xausa_, Jan 22 2025 *)
%Y A372026 Cf. A002378, A152811, A371912 (Zagreb indices of maximal k-degenerate graphs).
%Y A372026 Cf. A051624, A372025, A372026 (second Zagreb indices of maximal k-degenerate graphs).
%Y A372026 Cf. A372027 (second Zagreb index of MOPs).
%K A372026 nonn
%O A372026 3,1
%A A372026 _Allan Bickle_, Apr 16 2024