

A132759


a(n) = n(n+13).


13



0, 14, 30, 48, 68, 90, 114, 140, 168, 198, 230, 264, 300, 338, 378, 420, 464, 510, 558, 608, 660, 714, 770, 828, 888, 950, 1014, 1080, 1148, 1218, 1290, 1364, 1440, 1518, 1598, 1680, 1764, 1850, 1938, 2028, 2120, 2214, 2310, 2408
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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


REFERENCES

F. P. Muga II, Extending the Golden Ratio and the Binetde Moivre Formula, March 2014; Preprint on ResearchGate.


LINKS

Table of n, a(n) for n=0..43.
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(n1) + 12 (with a(0)=0).  Vincenzo Librandi, Aug 03 2010
G.f. 2*x*(7+6*x) / (x1)^3 .  R. J. Mathar, Jul 14 2012
sum_{n>=1} 1/a(n) = 1145993/4684680 = 0.2446256...  R. J. Mathar, Jul 14 2012


MATHEMATICA

s=0; lst={s}; Do[s+=n++ +14; AppendTo[lst, s], {n, 0, 7!, 2}]; lst (* Vladimir Joseph Stephan Orlovsky, Nov 19 2008 *)


PROG

(PARI) a(n)=n*(n+13) \\ Charles R Greathouse IV, Sep 24 2015


CROSSREFS

Cf. A002378, A120071.
Sequence in context: A055039 A044075 A044456 * A011257 A083540 A027575
Adjacent sequences: A132756 A132757 A132758 * A132760 A132761 A132762


KEYWORD

easy,nonn


AUTHOR

Omar E. Pol, Aug 28 2007


STATUS

approved



