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A278125
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a(n) = 225*2^n - 235.
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1
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-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
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0,1
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COMMENTS
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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.
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LINKS
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FORMULA
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G.f.: 5*(-2 + 49*x)/((1 - x)*(1 - 2*x).
a(n) = 3*a(n-1) - 2*a(n-2).
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MAPLE
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seq(225*2^n-235, n = 0..35)
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MATHEMATICA
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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 *)
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CROSSREFS
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KEYWORD
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sign,easy
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AUTHOR
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STATUS
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approved
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