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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 (list; graph; refs; listen; history; text; internal format)
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 Binet-de 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(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

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

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Last modified October 19 10:51 EDT 2019. Contains 328216 sequences. (Running on oeis4.)