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A304388
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a(n) = 144*2^n - 20 (n>=1).
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2
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268, 556, 1132, 2284, 4588, 9196, 18412, 36844, 73708, 147436, 294892, 589804, 1179628, 2359276, 4718572, 9437164, 18874348, 37748716, 75497452, 150994924, 301989868, 603979756, 1207959532, 2415919084, 4831838188, 9663676396, 19327352812, 38654705644, 77309411308
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OFFSET
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1,1
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COMMENTS
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a(n) is the second Zagreb index of the dendrimer nanostar NS1[n], defined pictorially in the Ashrafi et al. reference (Ns1[3] is shown in Fig. 1) or in the Ahmadi et al. reference (Fig. 1).
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 NS1[n] is M(NS1[n]; x,y) = xy^4 + (9*2^n +3)x^2*y^2 + (18*2^n - 12)x^2*y^3 + 3x^3*y^4.
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LINKS
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FORMULA
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G.f.: 4*x*(67 - 62*x) / ((1 - x)*(1 - 2*x)).
a(n) = 3*a(n-1) - 2*a(n-2) for n>2.
(End)
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MAPLE
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seq(144*2^n-20, n = 1 .. 40);
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MATHEMATICA
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LinearRecurrence[{3, -2}, {268, 556}, 30] (* Harvey P. Dale, Nov 02 2021 *)
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PROG
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(PARI) a(n) = 144*2^n - 20; \\ Altug Alkan, May 13 2018
(PARI) Vec(4*x*(67 - 62*x) / ((1 - x)*(1 - 2*x)) + O(x^40)) \\ Colin Barker, May 18 2018
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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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