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A228600
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The Szeged index of the n-sunlet graph (n>=3).
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1
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27, 92, 125, 282, 343, 632, 729, 1190, 1331, 2004, 2197, 3122, 3375, 4592, 4913, 6462, 6859, 8780, 9261, 11594, 12167, 14952, 15625, 18902, 19683, 23492, 24389, 28770, 29791, 34784, 35937, 41582, 42875, 49212, 50653, 57722
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OFFSET
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3,1
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COMMENTS
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The n-sunlet graph is the graph on 2n vertices obtained by attaching a pendant edge to each vertex of the cycle graph C_n.
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REFERENCES
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M. V. Diudea, I. Gutman, J. Lorentz, Molecular Topology, Nova Science, 2001, Huntington, N.Y. p. 151.
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LINKS
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FORMULA
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a(n) = 4*n*(floor(n/2))^2 +2*n^2 - n.
a(n) = n^3 if n is odd; a(n) = n^3 + 2*n^2 -n if n is even.
G.f.: x^3*(27+65*x-48*x^2-38*x^3+43*x^4+13*x^5-14*x^6)/((1+x)^3*(1-x)^4).
If we attach r pendant edges to each vertex of the cycle graph C_n, then the obtained graph has Szeged index n(r+1)^2*(floor(n/2))^2 +(nr)^2 + n^2*r - nr.
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MAPLE
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a := proc (n) options operator, arrow: 4*n*floor((1/2)*n)^2+2*n^2-n end proc: seq(a(n), n = 3 .. 38);
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MATHEMATICA
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Table[If[OddQ[n], n^3, n^3+2n^2-n], {n, 3, 40}] (* or *) LinearRecurrence[ {1, 3, -3, -3, 3, 1, -1}, {27, 92, 125, 282, 343, 632, 729}, 40] (* Harvey P. Dale, Jul 23 2016 *)
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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