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 A296515 #167 Feb 16 2025 08:33:52
%S A296515 0,0,1,3,6,9,12,15,18,21,24,27,30,33,36,39,42,45,48,51,54,57,60,63,66,
%T A296515 69,72,75,78,81,84,87,90,93,96,99,102,105,108,111,114,117,120,123,126,
%U A296515 129,132,135,138,141,144,147,150,153,156,159,162,165,168,171,174
%N A296515 Number of edges in a maximal planar graph with n vertices.
%C A296515 {a(n)} is a monotonic increasing sequence because a maximal planar graph of order n can be generated on n + 1 nodes. Therefore a(n) <= a(n + 1).
%C A296515 Maximal planar graphs of order n > 5 are not unique.
%C A296515 |E(G_2n)| = (2n - 1) + 2*Sum_{k=0..(floor(log_2(n - 1)))} floor((n - 1)/2^k) where |E(G_2n)| is the size of a minimal planar graph G of order 2n.
%C A296515 Number of edges of a maximal 3-degenerate graph of order n (this class includes 3-trees). The intersection of this class and maximal planar graphs is the Apollonian networks (planar 3-trees); neither class contains the other. - _Allan Bickle_, Nov 14 2021
%C A296515 a(n) is the number of blocks to dig (in a staircase fashion) to get out of a hole of depth n in Minecraft. - _Max R Anderson_, Oct 19 2023
%H A296515 Stefano Spezia, <a href="/A296515/b296515.txt">Table of n, a(n) for n = 0..10000</a>
%H A296515 Allan Bickle, <a href="https://doi.org/10.7151/dmgt.1637">Structural results on maximal k-degenerate graphs</a>, Discuss. Math. Graph Theory 32 4 (2012), 659-676.
%H A296515 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 A296515 Dawei He, Yan Wang, and Xingxing Yu, <a href="https://arxiv.org/abs/1511.05020">The Kelmans-Seymour conjecture I</a>, arXiv:1511.05020 [math.CO], 2015.
%H A296515 D. R. Lick and A. T. White, <a href="https://doi.org/10.4153/CJM-1970-125-1">k-degenerate graphs</a>, Canad. J. Math. 22 (1970), 1082-1096.
%H A296515 Mathematics Stack Exchange, <a href="https://math.stackexchange.com/questions/4673541/you-dig-a-hole-in-minecraft-straight-down-n-blocks-how-many-blocks-must-you-d">You dig a hole in Minecraft straight down n blocks, how many blocks must you dig to get out?</a>
%H A296515 K. Stephenson, <a href="http://www.ams.org/notices/200311/fea-stephenson.pdf">Circle Packing: A Mathematical Tale</a>, Notices Amer. Math. Soc. 50 (2003).
%H A296515 Squid Tamar-Mattis, <a href="http://math.uchicago.edu/~may/REU2016/REUPapers/Tamar-Mattis.pdf">Planar Graphs and Wagner's and Kuratowski's Theorems</a>, REU (2016).
%H A296515 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/KuratowskiReductionTheorem.html">Kuratowski Reduction Theorem</a>, <a href="https://mathworld.wolfram.com/PolyhedralGraph.html">Polyhedral Graph</a>
%H A296515 David R. Wood, <a href="https://arxiv.org/abs/cs/0505047">A Simple Proof of the Fary-Wagner Theorem</a>, arXiv:cs/0505047 [math.CO], 2005.
%H A296515 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (2,-1).
%F A296515 a(n) = floor(6/2^n) + 3n - 6 (see comments section of A008486).
%F A296515 G.f.: x^2 + 3*x^3/(x - 1)^2. - _R. J. Mathar_, Apr 14 2018
%F A296515 E.g.f.: 6 + x*(x + 6)/2 + 3*exp(x)*(x - 2). - _Stefano Spezia_, Feb 13 2023
%F A296515 a(n) = 3*(n - 2) for n >= 3. - _Max R Anderson_, Oct 19 2023
%t A296515 CoefficientList[Series[(x^2 (1 + x + x^2))/(x - 1)^2, {x, 0, 60}], x] (* or *) LinearRecurrence[{2, -1}, {0, 0, 1, 3}, 60] (* _Robert G. Wilson v_, Mar 04 2018 *)
%Y A296515 Cf. A008486, A008585, A242088.
%K A296515 nonn,easy
%O A296515 0,4
%A A296515 _Joseph Wheat_, _Jonathan Sondow_, Feb 28 2018