cp's OEIS Frontend

A305272 a(n) = 836*2^n - 676.

%I A305272 #17 Jun 19 2021 19:14:35
%S A305272 160,996,2668,6012,12700,26076,52828,106332,213340,427356,855388,
%T A305272 1711452,3423580,6847836,13696348,27393372,54787420,109575516,
%U A305272 219151708,438304092,876608860,1753218396,3506437468,7012875612,14025751900,28051504476,56103009628,112206019932,224412040540,448824081756
%N A305272 a(n) = 836*2^n - 676.
%C A305272 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).
%C A305272 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.
%C A305272 The M-polynomial 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.
%H A305272 Colin Barker, <a href="/A305272/b305272.txt">Table of n, a(n) for n = 0..1000</a>
%H A305272 N. E. Arif, Roslan Hasni and Saeid Alikhani, <a href="http://dx.doi.org/10.3923/jas.2012.2279.2282">Fourth order and fourth sum connectivity indices of polyphenylene dendrimers</a>, J. Applied Science, 12 (21), 2012, 2279-2282.
%H A305272 E. Deutsch and Sandi Klavzar, <a href="http://dx.doi.org/10.22052/ijmc.2015.10106">M-polynomial and degree-based topological indices</a>, Iranian J. Math. Chemistry, 6, No. 2, 2015, 93-102.
%H A305272 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (3,-2).
%F A305272 From _Colin Barker_, May 31 2018: (Start)
%F A305272 G.f.: 4*(40 + 129*x) / ((1 - x)*(1 - 2*x)).
%F A305272 a(n) = 3*a(n-1) - 2*a(n-2) for n>1.
%F A305272 (End)
%p A305272 seq(836*2^n-676, n = 0..40);
%t A305272 836*2^Range[0,40]-676 (* or  *) LinearRecurrence[{3,-2},{160,996},40] (* _Harvey P. Dale_, Jun 19 2021 *)
%o A305272 (PARI) Vec(4*(40 + 129*x) / ((1 - x)*(1 - 2*x)) + O(x^40)) \\ _Colin Barker_, May 31 2018
%Y A305272 Cf. A305269, A305270, A305271.
%K A305272 nonn,easy
%O A305272 0,1
%A A305272 _Emeric Deutsch_, May 30 2018