A238777 a(n) = floor((5^n+1)/(2*3^n)).

1, 1, 2, 3, 6, 10, 17, 29, 49, 82, 137, 229, 382, 638, 1063, 1772, 2953, 4923, 8205, 13675, 22792, 37987, 63312, 105521, 175868, 293114, 488524, 814207, 1357012, 2261686, 3769478, 6282463, 10470772, 17451288, 29085480

Offset: 1

Author

Kival Ngaokrajang, Mar 05 2014

Keywords

• nonn

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

Crossrefs

Cf. A000351, A034478.

Programs

Magma

[Floor((5^n+1)/(2*3^n)): n in [1..40]]; // Vincenzo Librandi, Mar 11 2014

Maple

A238777:=n->floor((5^n+1)/(2*3^n)); seq(A238777(n), n=1..50); # Wesley Ivan Hurt, Mar 09 2014

Mathematica

Table[Floor[(5^n + 1)/(2*3^n)], {n, 50}] (* Wesley Ivan Hurt, Mar 09 2014 *)

PARI

vector(100, n, floor((5^n+1)/(2*3^n))) \\ Colin Barker, Mar 05 2014

Formula

a(n) = A034478(n)/3^n.