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 A132759 #44 Feb 16 2025 08:33:06
%S A132759 0,14,30,48,68,90,114,140,168,198,230,264,300,338,378,420,464,510,558,
%T A132759 608,660,714,770,828,888,950,1014,1080,1148,1218,1290,1364,1440,1518,
%U A132759 1598,1680,1764,1850,1938,2028,2120,2214,2310,2408
%N A132759 a(n) = n*(n+13).
%C A132759 a(n) is the first Zagreb index of the gear graph g[n]. The first Zagreb index of a simple connected graph is the sum of the squared degrees of its vertices. Alternately, it is the sum of the degree sums d(i) + d(j) over all edges ij of the graph. The gear graph g[n] is defined as a wheel graph with n+1 vertices with a vertex added between each pair of adjacent vertices of the outer cycle. - _Emeric Deutsch_, Nov 09 2016
%H A132759 Felix P. Muga II, <a href="https://www.researchgate.net/publication/267327689">Extending the Golden Ratio and the Binet-de Moivre Formula</a>, Preprint on ResearchGate, March 2014.
%H A132759 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/GearGraph.html">Gear Graph</a>.
%H A132759 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (3,-3,1).
%F A132759 a(n) = n*(n + 13) = 2*A056119(n).
%F A132759 a(n) = 2*n + a(n-1) + 12 (with a(0)=0). - _Vincenzo Librandi_, Aug 03 2010
%F A132759 G.f.: 2*x*(-7+6*x)/(x-1)^3. - _R. J. Mathar_, Jul 14 2012
%F A132759 Sum_{n>=1} 1/a(n) = 1145993/4684680 = 0.2446256... - _R. J. Mathar_, Jul 14 2012
%F A132759 Sum_{n>=1} (-1)^(n+1)/a(n) = 2*log(2)/13 - 263111/4684680. - _Amiram Eldar_, Jan 15 2021
%F A132759 From _Elmo R. Oliveira_, Dec 12 2024: (Start)
%F A132759 E.g.f.: exp(x)*x*(14 + x).
%F A132759 a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3) for n > 2. (End)
%t A132759 s=0;lst={s};Do[s+=n++ +14;AppendTo[lst, s], {n, 0, 7!, 2}];lst (* _Vladimir Joseph Stephan Orlovsky_, Nov 19 2008 *)
%t A132759 Table[n(n+13),{n,0,50}] (* _Harvey P. Dale_, Aug 22 2019 *)
%o A132759 (PARI) a(n)=n*(n+13) \\ _Charles R Greathouse IV_, Sep 24 2015
%Y A132759 Cf. A002378, A056119, A120071.
%K A132759 easy,nonn
%O A132759 0,2
%A A132759 _Omar E. Pol_, Aug 28 2007