

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
Conjecture: satisfies a linear recurrence having signature (3, 3, 1).  Harvey P. Dale, Aug 22 2019


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 *)
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

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



