A255216 a(n) = floor((3/sqrt(5))^n).

1, 1, 1, 2, 3, 4, 5, 7, 10, 14, 18, 25, 34, 45, 61, 82, 110, 147, 198, 266, 357, 479, 642, 862, 1156, 1552, 2082, 2793, 3748, 5028, 6746, 9051, 12143, 16292, 21859, 29327, 39346, 52788, 70823, 95019, 127482, 171035, 229468, 307863, 413042, 554155, 743477, 997479, 1338258

Offset: 0

Author

Kival Ngaokrajang, Feb 25 2015

Keywords

• nonn

Comments

a(n) is the total length (rounded down to integer) of the elements of a variant of a 3-element fractal after n iterations, starting with 3 elements, each of whose length is 1/3 (in some units). See illustration in the links.

Links

• Harvey P. Dale, Table of n, a(n) for n = 0..1000
• Kival Ngaokrajang, Illustration of initial terms

Crossrefs

Cf. A017919.

Programs

Mathematica

With[{c=3/Sqrt[5]},Table[Floor[c^n],{n,0,50}]] (* Harvey P. Dale, Oct 23 2023 *)

PARI

{for(n=0,100,a=floor((3/sqrt(5))^n);print1(a,", "))}

Formula

a(n) = floor((3/sqrt(5))^n).