A229977 Gosper island perimeter (rounded to the nearest integer) after n iterations, let starting perimeter = 1.

1, 1, 1, 1, 2, 2, 2, 2, 3, 3, 4, 4, 5, 5, 6, 7, 7, 8, 10, 11, 12, 14, 16, 18, 20, 23, 26, 30, 34, 38, 43, 49, 56, 63, 72, 81, 92, 105, 119, 134, 152, 173, 196, 222, 252, 286, 324, 367, 416, 472, 535, 607, 688, 780, 885, 1003

Offset: 0

Author

Kival Ngaokrajang, Oct 05 2013

Keywords

• nonn

Comments

The Gosper island curve bounds the space filled by the Peano-Gosper curve. The length of Peano-Gosper curve after n iterations (rounded to the nearest integer) is A017926(n) and the total number of elements is A000420(n). See illustration in links.

The sequence expansion ratio (a(n)/a(n-1)) is 1.133893419... which is 3*A020764.

Links

• Kival Ngaokrajang, Illustration of initial terms
• Eric Weisstein's World of Mathematics, Gosper Island

Crossrefs

Cf. A017926, A000420, A227381 (Koch snowflake perimeter).

Formula

a(n) = round((3/sqrt(7))^n).