OFFSET
1,3
COMMENTS
a(n) is the rounded-down perimeter of the Vicsek fractal after n iterations. The Vicsek fractal is a subset of the box fractal; for both types, the number of boxes = A000351(n). See illustrations in links.
LINKS
Vincenzo Librandi, Table of n, a(n) for n = 1..1000
Kival Ngaokrajang, Illustrations of initial terms
Eric Weisstein's World of Mathematics, Box Fractal
Wikipedia, Vicsek Fractal
FORMULA
a(n) = A034478(n)/3^n.
MAPLE
MATHEMATICA
Table[Floor[(5^n + 1)/(2*3^n)], {n, 50}] (* Wesley Ivan Hurt, Mar 09 2014 *)
PROG
(Small Basic)
For n = 1 to 40
x = (math.Power(5, n)+1)/(2*math.Power(3, n))
a = math.Floor(x)
TextWindow.Write(a+", ")
Endfor
(PARI)
vector(100, n, floor((5^n+1)/(2*3^n))) \\ Colin Barker, Mar 05 2014
(Magma) [Floor((5^n+1)/(2*3^n)): n in [1..40]]; // Vincenzo Librandi, Mar 11 2014
CROSSREFS
KEYWORD
nonn
AUTHOR
Kival Ngaokrajang, Mar 05 2014
STATUS
approved