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A305154
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a(n) = 36*2^n + 9.
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1
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45, 81, 153, 297, 585, 1161, 2313, 4617, 9225, 18441, 36873, 73737, 147465, 294921, 589833, 1179657, 2359305, 4718601, 9437193, 18874377, 37748745, 75497481, 150994953, 301989897, 603979785, 1207959561, 2415919113, 4831838217, 9663676425, 19327352841, 38654705673, 77309411337, 154618822665, 309237645321
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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 dendrimer D[n], defined pictorially in Fig. 1 of the Heydari et al. reference.
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 M-polynomial of D[n] is M(D[n]; x, y) = 3*2^n*x*y^3 + 6*x^2*y^3 + 3*(2^n - 1)*x^3*y^3 (n>=0).
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LINKS
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FORMULA
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G.f.: 9*(5 - 6*x)/((1 - 2*x)*(1 - x)).
a(n) = 3*a(n-1) - 2*a(n-2). (End)
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MAPLE
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seq(36*2^n + 9, n = 0..40);
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MATHEMATICA
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LinearRecurrence[{3, -2}, {45, 81}, 40] (* Harvey P. Dale, Jan 08 2020 *)
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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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