OFFSET
0,2
COMMENTS
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
LINKS
Felix P. Muga II, Extending the Golden Ratio and the Binet-de Moivre Formula, Preprint on ResearchGate, March 2014.
Eric Weisstein's World of Mathematics, Gear Graph.
Index entries for linear recurrences with constant coefficients, signature (3,-3,1).
FORMULA
a(n) = n*(n + 13) = 2*A056119(n).
a(n) = 2*n + a(n-1) + 12 (with a(0)=0). - Vincenzo Librandi, Aug 03 2010
G.f.: 2*x*(-7+6*x) / (x-1)^3 . - R. J. Mathar, Jul 14 2012
Sum_{n>=1} 1/a(n) = 1145993/4684680 = 0.2446256... - R. J. Mathar, Jul 14 2012
Sum_{n>=1} (-1)^(n+1)/a(n) = 2*log(2)/13 - 263111/4684680. - Amiram Eldar, Jan 15 2021
MATHEMATICA
s=0; lst={s}; Do[s+=n++ +14; AppendTo[lst, s], {n, 0, 7!, 2}]; lst (* Vladimir Joseph Stephan Orlovsky, Nov 19 2008 *)
Table[n(n+13), {n, 0, 50}] (* Harvey P. Dale, Aug 22 2019 *)
PROG
(PARI) a(n)=n*(n+13) \\ Charles R Greathouse IV, Sep 24 2015
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
Omar E. Pol, Aug 28 2007
STATUS
approved