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A241038 a(n) = A000217(A058481(n)). 1
0, 1, 28, 325, 3160, 29161, 264628, 2388205, 21513520, 193680721, 1743303628, 15690264085, 141213971080, 1270930522681, 11438389053028, 102945544523965, 926510029855840, 8338590656123041, 75047317067368828 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,3
COMMENTS
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.
LINKS
FORMULA
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
MAPLE
A241038:=n->(1/2)*3^(2*n) - (3/2)*3^n + 1; seq(A241038(n), n=0..30); # Wesley Ivan Hurt, Apr 15 2014
MATHEMATICA
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 *)
PROG
(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
CROSSREFS
Sequence in context: A042520 A022688 A125416 * A055753 A159520 A027820
KEYWORD
nonn,easy
AUTHOR
Kival Ngaokrajang, Apr 15 2014
STATUS
approved

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Last modified April 13 15:06 EDT 2024. Contains 371644 sequences. (Running on oeis4.)