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A241271
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a(n) = 6*a(n-1) + 3*(2^(n-2)-1) for n > 2, a(0)=a(1)=a(2)=0.
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3
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0, 0, 0, 3, 27, 183, 1143, 6951, 41895, 251751, 1511271, 9069159, 54418023, 326514279, 1959097959, 11754612327, 70527723111, 423166436967, 2538998818407, 15233993303655, 91403960608359, 548423765223015, 3290542594483815, 19743255573194343, 118459533451748967
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OFFSET
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0,4
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COMMENTS
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a(n) is the total number of irregular polygon holes of a triflake-like fractal (A240916) after n iterations. A240916(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) = (24-15*2^n+6^n)/40 for n>0. G.f.: -3*x^3 / ((x-1)*(2*x-1)*(6*x-1)). - Colin Barker, Apr 18 2014
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MAPLE
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MATHEMATICA
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CoefficientList[Series[-3 x^3/((x - 1) (2 x - 1) (6 x - 1)), {x, 0, 40}], x] (* Vincenzo Librandi, Apr 19 2014 *)
LinearRecurrence[{9, -20, 12}, {0, 0, 0, 3}, 30] (* Harvey P. Dale, Dec 28 2021 *)
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PROG
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(PARI) a(n) = if(n<=0, 0, if(n<2, 0, if(n<3, 0, a(n-1)*6+3*(2^(n-2)-1))))
for(n=0, 100, print1(a(n), ", "))
(PARI) concat([0, 0, 0], Vec(-3*x^3/((x-1)*(2*x-1)*(6*x-1)) + O(x^100))) \\ Colin Barker, Apr 18 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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