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A132761 a(n) = n*(n+17). 18
0, 18, 38, 60, 84, 110, 138, 168, 200, 234, 270, 308, 348, 390, 434, 480, 528, 578, 630, 684, 740, 798, 858, 920, 984, 1050, 1118, 1188, 1260, 1334, 1410, 1488, 1568, 1650, 1734, 1820, 1908, 1998, 2090, 2184, 2280, 2378, 2478, 2580 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

a(n) is the first Zagreb index of the helm graph H[n] (n>=3). - Emeric Deutsch, Nov 05 2016

From Emeric Deutsch, Nov 07 2016: (Start)

a(n) is the first Zagreb index of the graph obtained by joining one vertex of the cycle graph C[n] with each vertex of a second cycle graph C[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. (End)

From Emeric Deutsch, May 11 2018: (Start)

The M-polynomial of the Helm graph H[n] is M(H[n];x,y) = n*x*y^4 + n*x^4*y^4 + n*x^4*y^n.

The helm graph H[n] is the graph obtained from an n-wheel graph by adjoining a pendant edge at each node of the cycle. (End)

LINKS

Muniru A Asiru, Table of n, a(n) for n = 0..5000

E. Deutsch and Sandi Klavzar, M-polynomial and degree-based topological indices, Iranian J. Math. Chemistry, 6, No. 2, 2015, 93-102.

I. Gutman and K. C. Das, The first Zagreb index 30 years after, MATCH Commun. Math. Comput. Chem. 50, 2004, 83-92.

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

Eric Weisstein's World of Mathematics, Helm Graph

Index entries for linear recurrences with constant coefficients, signature (3,-3,1).

FORMULA

a(n) = n*(n + 17).

a(n) = A132760(n) + 2*n = A132765(n) - 6*n = A098849(n) + 1*n = A120071(n) - 3*n. - Zerinvary Lajos, Feb 17 2008

a(n) = 2*n + a(n-1) + 16 for n>0, a(0)=0. - Vincenzo Librandi, Aug 03 2010

G.f.: 2*x*(9 - 8*x)/(1 - x)^3. - Emeric Deutsch, Nov 07 2016

PROG

(PARI) a(n)=n*(n+17) \\ Charles R Greathouse IV, Nov 07 2016

(GAP) List([0..50], n->n*(n+17)); # Muniru A Asiru, May 11 2018

CROSSREFS

Cf. A002378, A120071, A098849, A132760, A132765.

Sequence in context: A119127 A190739 A084585 * A079862 A106521 A070686

Adjacent sequences:  A132758 A132759 A132760 * A132762 A132763 A132764

KEYWORD

nonn,easy

AUTHOR

Omar E. Pol, Aug 28 2007

STATUS

approved

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Last modified March 20 15:43 EDT 2019. Contains 321345 sequences. (Running on oeis4.)