

A305272


a(n) = 836*2^n  676.


4



160, 996, 2668, 6012, 12700, 26076, 52828, 106332, 213340, 427356, 855388, 1711452, 3423580, 6847836, 13696348, 27393372, 54787420, 109575516, 219151708, 438304092, 876608860, 1753218396, 3506437468, 7012875612, 14025751900, 28051504476, 56103009628, 112206019932, 224412040540, 448824081756
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OFFSET

0,1


COMMENTS

a(n) is the second Zagreb index of the polyphenylene dendrimer G[n], defined pictorially in the Arif et al. reference (see Fig. 1, where G[2] is shown).
The second Zagreb index of a simple connected graph is the sum of the degree products d(i)d(j) over all edges ij of the graph.
The Mpolynomial of the polyphenylene dendrimer G[n] is M(G[n]; x, y) = (56*2^n  40)*x^2*y^2 + (48*2^n  40)*x^2*y^3 +(36* 2^n  36)*x^3*y^3 + 4*x^3 *y^4.


LINKS



FORMULA

G.f.: 4*(40 + 129*x) / ((1  x)*(1  2*x)).
a(n) = 3*a(n1)  2*a(n2) for n>1.
(End)


MAPLE

seq(836*2^n676, n = 0..40);


MATHEMATICA

836*2^Range[0, 40]676 (* or *) LinearRecurrence[{3, 2}, {160, 996}, 40] (* Harvey P. Dale, Jun 19 2021 *)


PROG

(PARI) Vec(4*(40 + 129*x) / ((1  x)*(1  2*x)) + O(x^40)) \\ Colin Barker, May 31 2018


CROSSREFS



KEYWORD

nonn,easy


AUTHOR



STATUS

approved



