

A278125


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


1



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
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OFFSET

0,1


COMMENTS

a(n) is the second Zagreb index of the Wang's helicenebased 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 Mpolynomial of the Wang's helicenebased 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



FORMULA

G.f.: 5*(2 + 49*x)/((1  x)*(1  2*x).
a(n) = 3*a(n1)  2*a(n2).


MAPLE

seq(225*2^n235, 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



KEYWORD

sign,easy


AUTHOR



STATUS

approved



