A241038 a(n) = A000217(A058481(n)).

0, 1, 28, 325, 3160, 29161, 264628, 2388205, 21513520, 193680721, 1743303628, 15690264085, 141213971080, 1270930522681, 11438389053028, 102945544523965, 926510029855840, 8338590656123041, 75047317067368828

Offset: 0

Author

Kival Ngaokrajang, Apr 15 2014

Keywords

• nonn
• easy

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

• Kival Ngaokrajang, Illustration of initial terms
• Index entries for linear recurrences with constant coefficients, signature (13,-39,27).

Crossrefs

Cf. A000217, A058481, A240917.

Programs

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 *)

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

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