A278124 - OEIS

A278124

a(n) = 172*2^n - 176.

-4, 168, 512, 1200, 2576, 5328, 10832, 21840, 43856, 87888, 175952, 352080, 704336, 1408848, 2817872, 5635920, 11272016, 22544208, 45088592, 90177360, 180354896, 360709968, 721420112, 1442840400, 2885680976, 5771362128, 11542724432, 23085449040, 46170898256, 92341796688, 184683593552

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OFFSET

0,1

COMMENTS

a(n) is the first Zagreb index of the Wang's helicene-based nanostar DNS[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. The pictorial definition of DNS[n] can be viewed in the H. Shabani A. R. et al. reference (it is denoted DNS_{2}[n]).

The M-polynomial of the Wang's helicene-based dendrimer DNS[n] is M(DNS[n],x,y) = (2*2^n - 1)*x*y^3 + (6*2^n -4)*x^2*y^2 + (10*2^n - 12)*x^2*y^3 + (15*2^n - 16)*x^3*y^3.

REFERENCES

H. Shabani, A. R. Ashrafi, and I. Gutman, Geometric-arithmetic index: an algebraic approach, Studia UBB, Chemia, 55, No. 4, 107-112, 2010.

LINKS

Table of n, a(n) for n=0..30.

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.

Index entries for linear recurrences with constant coefficients, signature (3,-2)

FORMULA

G.f.: 4*(-1 + 45*x)/((1 - x)*(1 - 2*x).

a(n) = 3*a(n-1) - 2*a(n-2).

MAPLE

seq(172*2^n-176, n = 0 .. 35);