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A277107
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a(n) = 16*3^n - 48.
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1
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0, 96, 384, 1248, 3840, 11616, 34944, 104928, 314880, 944736, 2834304, 8503008, 25509120, 76527456, 229582464, 688747488, 2066242560, 6198727776, 18596183424, 55788550368, 167365651200, 502096953696, 1506290861184, 4518872583648, 13556617751040
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OFFSET
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1,2
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COMMENTS
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a(n) is the second Zagreb index of the Sierpiński [Sierpinski] sieve graph S[n] (n>=2).
The second Zagreb index of a simple connected graph g is the sum of the degree products d(i)d(j) over all edges ij of g.
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.: 96*x^2/((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(16*3^n-48, n = 1..30);
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MATHEMATICA
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Table[16*3^n - 48, {n, 25}] (* or *) Rest@ CoefficientList[Series[96 x^2/((1 - x) (1 - 3 x)), {x, 0, 25}], x] (* Michael De Vlieger, Nov 06 2016 *)
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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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