

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
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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 Mpolynomial 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 nwheel 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, Mpolynomial and degreebased topological indices, Iranian J. Math. Chemistry, 6, No. 2, 2015, 93102.
I. Gutman and K. C. Das, The first Zagreb index 30 years after, MATCH Commun. Math. Comput. Chem. 50, 2004, 8392.
F. P. Muga II, Extending the Golden Ratio and the Binetde 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(n1) + 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



