A278125 a(n) = 225*2^n - 235.

-10, 215, 665, 1565, 3365, 6965, 14165, 28565, 57365, 114965, 230165, 460565, 921365, 1842965, 3686165, 7372565, 14745365, 29490965, 58982165, 117964565, 235929365, 471858965, 943718165, 1887436565, 3774873365, 7549746965, 15099494165, 30198988565, 60397977365, 120795954965

Offset

0,1

Comments

a(n) is the second Zagreb index of the Wang's helicene-based nanostar DNS[n]. 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 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.

Links

Table of n, a(n) for n=0..29.

E. Deutsch and Sandi Klavzar, M-polynomial and degree-based topological indices, Iranian J. Math. Chemistry, 6, No. 2, 2015, 93-102.

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

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

Formula

G.f.: 5*(-2 + 49*x)/((1 - x)*(1 - 2*x).

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

Maple

seq(225*2^n-235, n = 0..35)

Mathematica

Table[225*2^n - 235, {n, 0, 12}] (* or *)
CoefficientList[Series[5 (49 x - 2)/((1 - x) (1 - 2 x)), {x, 0, 12}], x] (* Michael De Vlieger, Nov 14 2016 *)
LinearRecurrence[{3, -2}, {-10, 215}, 30] (* Harvey P. Dale, May 28 2020 *)

Crossrefs

Cf. A278124.

Sequence in context: A309737 A211912 A213788 * A274763 A002967 A243476

Adjacent sequences: A278122 A278123 A278124 * A278126 A278127 A278128

Keyword

sign,easy

Author

Emeric Deutsch, Nov 13 2016

Status

approved