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0, 1, 28, 325, 3160, 29161, 264628, 2388205, 21513520, 193680721, 1743303628, 15690264085, 141213971080, 1270930522681, 11438389053028, 102945544523965, 926510029855840, 8338590656123041, 75047317067368828
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OFFSET
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0,3
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COMMENTS
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a(n) is the total number of hexagon holes in triflake-like fractal (A240917) after n iterations. A240917(n) - a(n) is the total number of rhombic holes.
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LINKS
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FORMULA
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a(n) = (1/2)*3^(2*n) - (3/2)*3^n + 1.
a(n) = 13*a(n-1)-39*a(n-2)+27*a(n-3). G.f.: -x*(15*x+1) / ((x-1)*(3*x-1)*(9*x-1)). - Colin Barker, Apr 15 2014
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MAPLE
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MATHEMATICA
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Table[(1/2)*3^(2 n) - (3/2)*3^n + 1, {n, 0, 30}] (* Wesley Ivan Hurt, Apr 15 2014 *)
LinearRecurrence[{13, -39, 27}, {0, 1, 28}, 30] (* Harvey P. Dale, Oct 12 2017 *)
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PROG
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(PARI) a(n)= (1/2)*3^(2*n) - (3/2)*3^n + 1
for(n=0, 100, print1(a(n), ", "))
(PARI) Vec(-x*(15*x+1)/((x-1)*(3*x-1)*(9*x-1)) + O(x^100)) \\ Colin Barker, Apr 15 2014
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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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