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

0,4

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

Formula

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

Mathematica

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

Prog

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

Crossrefs

Cf. A017919.

Sequence in context: A195944 A087830 A039857 * A017836 A321481 A238874

Adjacent sequences: A255213 A255214 A255215 * A255217 A255218 A255219

Keyword

nonn

Author

Kival Ngaokrajang, Feb 25 2015

Status

approved