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A277981
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a(n) = 4*n^2 + 18*n - 20.
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1
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-20, 2, 32, 70, 116, 170, 232, 302, 380, 466, 560, 662, 772, 890, 1016, 1150, 1292, 1442, 1600, 1766, 1940, 2122, 2312, 2510, 2716, 2930, 3152, 3382, 3620, 3866, 4120, 4382, 4652, 4930, 5216, 5510, 5812, 6122, 6440, 6766, 7100, 7442, 7792, 8150
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OFFSET
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0,1
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COMMENTS
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For n>=3, a(n) is the first Zagreb index of the uniform bow graph B[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 uniform bow graph B[n] consists of two path graphs P[n] and an additional vertex joined by 2n edges to the vertices of the paths.
The M-polynomial of the uniform bow graph B[n] is M(B[n],x,y) = 4*x^2*y^3 + 4*x^2*y^{2*n} + (2*n-6)*x^3*y^3 + (2*n-4)*x^3*y^{2*n}.
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LINKS
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FORMULA
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O.g.f.: 2*(17*x^2 - 31*x + 10)/(x - 1)^3.
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MAPLE
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seq(4*n^2+18*n-20, n=0..40);
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MATHEMATICA
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PROG
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(Sage) [4*n^2+18*n-20 for n in range(50)] # Bruno Berselli, Nov 11 2016
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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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