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%I #40 Jan 15 2021 06:05:04
%S 0,14,30,48,68,90,114,140,168,198,230,264,300,338,378,420,464,510,558,
%T 608,660,714,770,828,888,950,1014,1080,1148,1218,1290,1364,1440,1518,
%U 1598,1680,1764,1850,1938,2028,2120,2214,2310,2408
%N a(n) = n*(n+13).
%C 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 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 Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/GearGraph.html">Gear Graph</a>.
%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (3,-3,1).
%F a(n) = n*(n + 13) = 2*A056119(n).
%F a(n) = 2*n + a(n-1) + 12 (with a(0)=0). - _Vincenzo Librandi_, Aug 03 2010
%F G.f.: 2*x*(-7+6*x) / (x-1)^3 . - _R. J. Mathar_, Jul 14 2012
%F Sum_{n>=1} 1/a(n) = 1145993/4684680 = 0.2446256... - _R. J. Mathar_, Jul 14 2012
%F Sum_{n>=1} (-1)^(n+1)/a(n) = 2*log(2)/13 - 263111/4684680. - _Amiram Eldar_, Jan 15 2021
%t s=0;lst={s};Do[s+=n++ +14;AppendTo[lst, s], {n, 0, 7!, 2}];lst (* _Vladimir Joseph Stephan Orlovsky_, Nov 19 2008 *)
%t Table[n(n+13),{n,0,50}] (* _Harvey P. Dale_, Aug 22 2019 *)
%o (PARI) a(n)=n*(n+13) \\ _Charles R Greathouse IV_, Sep 24 2015
%Y Cf. A002378, A056119, A120071.
%K easy,nonn
%O 0,2
%A _Omar E. Pol_, Aug 28 2007
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