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A305165
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a(n) = 136*2^n - 112.
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3
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24, 160, 432, 976, 2064, 4240, 8592, 17296, 34704, 69520, 139152, 278416, 556944, 1114000, 2228112, 4456336, 8912784, 17825680, 35651472, 71303056, 142606224, 285212560, 570425232, 1140850576, 2281701264, 4563402640, 9126805392, 18253610896, 36507221904, 73014443920, 146028887952, 292057776016, 584115552144
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OFFSET
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0,1
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COMMENTS
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a(n) is the first Zagreb index of the second type dendrimer nanostar NS2[n], defined pictorially in the Chen et al. reference (Fig. 1).
The first Zagreb index of a simple connected graph is the sum of the squared degrees of its vertices. Alternatively, it is the sum of the degree sums d(i) + d(j) over all edges ij of the graph.
The M-polynomial of NS2[n] is M(NS2[n];x,y) = 2*(4*2^n-1)*x^2*y^2 + 16*(2*n - 1)*x^2*y^3 + 4*(2^n - 1)*x^3*y^3 (n>=0).
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LINKS
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FORMULA
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MAPLE
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seq(136*2^n-112, n = 0 .. 40);
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MATHEMATICA
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LinearRecurrence[{3, -2}, {24, 160}, 40] (* Harvey P. Dale, Jan 30 2023 *)
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PROG
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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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