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A277106
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a(n) = 8*3^n - 12.
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1
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12, 60, 204, 636, 1932, 5820, 17484, 52476, 157452, 472380, 1417164, 4251516, 12754572, 38263740, 114791244, 344373756, 1033121292, 3099363900, 9298091724, 27894275196, 83682825612, 251048476860, 753145430604, 2259436291836, 6778308875532
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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 Sierpiński [Sierpinski] Sieve graph S[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 Sierpinski Sieve graph S[n] is M(S[n],x,y) = 6*x^2*y^4 + (3^n - 6)*x^4*y^4.
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LINKS
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FORMULA
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G.f.: 12*x*(1 + x)/((1 - x)*(1 - 3*x)).
a(n) = 4*a(n-1) - 3*a(n-2).
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MAPLE
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seq(8*3^n-12, n = 1..30);
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MATHEMATICA
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LinearRecurrence[{4, -3}, {12, 60}, 40] (* Harvey P. Dale, Oct 25 2020 *)
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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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