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A277104
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a(n) = 9*3^n - 15.
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1
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12, 66, 228, 714, 2172, 6546, 19668, 59034, 177132, 531426, 1594308, 4782954, 14348892, 43046706, 129140148, 387420474, 1162261452, 3486784386, 10460353188, 31381059594, 94143178812, 282429536466, 847288609428, 2541865828314, 7625597484972, 22876792454946
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OFFSET
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1,1
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COMMENTS
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a(n) is the first Zagreb index of the Hanoi graph H[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 M-polynomial of the Hanoi graph H[n] is M(H[n],x,y) = 6*x^2*y^3 + (3/2)*(3^n - 5)*x^3*y^3.
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LINKS
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FORMULA
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O.g.f.: 6*x*(2 + 3*x)/((1 - x)*(1 - 3*x)).
E.g.f.: 3*(1 - exp(x))*(2 - 3*exp(x) - 3*exp(2*x)). - Bruno Berselli, Nov 14 2016
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MAPLE
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seq(9*3^n-15, n = 1..30);
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MATHEMATICA
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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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