

A304165


a(n) = 324*n^2  336*n + 102 (n >= 1).


2



90, 726, 2010, 3942, 6522, 9750, 13626, 18150, 23322, 29142, 35610, 42726, 50490, 58902, 67962, 77670, 88026, 99030, 110682, 122982, 135930, 149526, 163770, 178662, 194202, 210390, 227226, 244710, 262842, 281622, 301050, 321126, 341850, 363222, 385242, 407910, 431226, 455190, 479802, 505062
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OFFSET

1,1


COMMENTS

a(n) is the first Zagreb index of the HcDN1(n) network (see Fig. 3 in the Hayat et al. manuscript).
The first Zagreb index of a simple connected graph is the sum of the squared degrees of its vertices. Alternatively, it is the sum of the degree sums d(i) + d(j) over all edges ij of the graph.
The Mpolynomial of HcDN1(n) is M(HcDN1(n);x,y) = 6x^3*y^3 + 12(n1)x^3*y^5 + 6nx^3*y^6 + 18(n1)x^5*y^6 + (27n^2 57n +30)x^6*y^6.  Emeric Deutsch, May 11 2018


LINKS

Colin Barker, Table of n, a(n) for n = 1..1000
E. Deutsch and Sandi Klavzar, Mpolynomial and degreebased topological indices, Iranian J. Math. Chemistry, 6, No. 2, 2015, 93102.
S. Hayat, M. A. Malik, and M. Imran, Computing topological indices of honeycomb derived networks, Romanian J. of Information Science and Technology, 18, No. 2, 2015, 144165.
Index entries for linear recurrences with constant coefficients, signature (3,3,1).


FORMULA

From Colin Barker, May 10 2018: (Start)
G.f.: 6*x*(15 + 76*x + 17*x^2) / (1  x)^3.
a(n) = 3*a(n1)  3*a(n2) + a(n3) for n>3.
(End)


MAPLE

seq(324*n^2336*n+102, n=1..40);


MATHEMATICA

Table[324n^2336n+102, {n, 40}] (* or *) LinearRecurrence[{3, 3, 1}, {90, 726, 2010}, 40] (* Harvey P. Dale, Apr 12 2020 *)


PROG

(PARI) a(n) = 324*n^2336*n+102; \\ Altug Alkan, May 09 2018
(PARI) Vec(6*x*(15 + 76*x + 17*x^2) / (1  x)^3 + O(x^60)) \\ Colin Barker, May 10 2018
(GAP) List([1..40], n>324*n^2336*n+102); # Muniru A Asiru, May 10 2018


CROSSREFS

Cf. A304163, A304164, A304166.
Sequence in context: A065949 A224541 A051695 * A232588 A097372 A263170
Adjacent sequences: A304162 A304163 A304164 * A304166 A304167 A304168


KEYWORD

nonn,easy


AUTHOR

Emeric Deutsch, May 09 2018


STATUS

approved



