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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 (list; graph; refs; listen; history; text; internal format)
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
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.
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
KEYWORD
sign,easy
AUTHOR
Emeric Deutsch, Nov 13 2016
STATUS
approved

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Last modified June 17 13:40 EDT 2024. Contains 373445 sequences. (Running on oeis4.)