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A305067
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a(n) = 282*2^n - 150.
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4
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132, 414, 978, 2106, 4362, 8874, 17898, 35946, 72042, 144234, 288618, 577386, 1154922, 2309994, 4620138, 9240426, 18481002, 36962154, 73924458, 147849066, 295698282, 591396714, 1182793578, 2365587306, 4731174762, 9462349674, 18924699498, 37849399146, 75698798442, 151397597034
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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 nanostar G[n], defined pictorially in the Iranmanesh et al. reference (Fig. 1, where G[3] is shown) or in Alikhani et al. reference (Fig. 1, where G[3] is shown).
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 G[n] is M(G[n]; x, y) = 3*2^n*x*y^3 + (12*2^n - 6)*x^2*y^2 + (24*2^n -12)*x^2*y^3 + (9*2^n - 6)*x^3*y^3.
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LINKS
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FORMULA
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G.f.: 6*x*(22 + 3*x) / ((1 - x)*(1 - 2*x)).
a(n) = 3*a(n-1) - 2*a(n-2) for n>1.
(End)
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MAPLE
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seq(282*2^n - 150, n = 0 .. 40);
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MATHEMATICA
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282*2^Range[0, 30]-150 (* or *) LinearRecurrence[{3, -2}, {132, 414}, 30] (* Harvey P. Dale, Apr 09 2023 *)
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PROG
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(PARI) Vec(6*x*(22 + 3*x) / ((1 - x)*(1 - 2*x)) + O(x^40)) \\ Colin Barker, May 25 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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