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A277988
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a(n) = 352*2^n + 34.
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1
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386, 738, 1442, 2850, 5666, 11298, 22562, 45090, 90146, 180258, 360482, 720930, 1441826, 2883618, 5767202, 11534370, 23068706, 46137378, 92274722, 184549410, 369098786, 738197538, 1476395042, 2952790050, 5905580066, 11811160098, 23622320162, 47244640290
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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 micelle-like chiral dendrimer B[n]. The first Zagreb index of a simple connected graph is the sum of the squared degrees of its vertices. Alternately, it is the sum of the degree sums d(i)+ d(j) over all edges ij of the graph. The pictorial definition of B[n] can be viewed in the Yousefi-Azari et al. references.
The M-polynomial of the micelle-like chiral dendrimer B[n] is M(B[n],x,y) = (8*2^n + 2)*x*y^2 + 12*x^2*y^2 + (56*2^n - 10)*x^2*y^3 + (8*2^n +5)*x^3*y^3.
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LINKS
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FORMULA
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G.f.: 2*(193 - 210*x)/((1-x)*(1-2*x)).
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MAPLE
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seq(352*2^n+34, n = 0..35);
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MATHEMATICA
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352*2^Range[0, 30]+34 (* or *) LinearRecurrence[{3, -2}, {386, 738}, 30] (* Harvey P. Dale, Jul 12 2021 *)
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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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