A228079 a(n) = round((5^n)*4 / 3^n).

4, 7, 11, 19, 31, 51, 86, 143, 238, 397, 662, 1103, 1838, 3063, 5104, 8507, 14179, 23631, 39386, 65643, 109404, 182341, 303901, 506502, 844170, 1406950, 2344917, 3908195, 6513658, 10856097, 18093496, 30155826, 50259710, 83766183, 139610306, 232683843

Offset

0,1

Comments

The nearest integer of perimeter of Cross-Stitch Curve (fractal) after n-th iteration starting with a unit square.

The total side segments after n-th iteration is (5^n)*4.

Links

Andrew Howroyd, Table of n, a(n) for n = 0..500

Kival Ngaokrajang, Illustration for n = 0..4

Eric Weisstein's World of Mathematics, Cross-Stitch Curve

Formula

a(n) = round(A000351(n)*4 / A000244(n)).

Example

For n = 1, the total sides = 4 * 5 = 20, each side length = 1/3, the perimeter = 20 * 1/3 = 6.666..; a(1) = 7.
For n = 2, the total sides = 4 * 5^2 = 100, each side length = 1/9, the perimeter = 100 * 1/9 = 11.111..; a(2) = 11.

Prog

(MIT/GNU Scheme)  (define (A228079 n) (round->exact (/ (* 4 (expt 5 n)) (expt 3 n)))) - Antti Karttunen, Aug 09 2013
(PARI) a(n) = {round((5^n)*4 / 3^n)} \\ Andrew Howroyd, Nov 05 2019

Crossrefs

Cf. A000351, A000244.

Sequence in context: A087203 A310768 A109328 * A083839 A091176 A002974

Adjacent sequences: A228076 A228077 A228078 * A228080 A228081 A228082

Keyword

nonn

Author

Kival Ngaokrajang, Aug 09 2013

Extensions

Terms a(23) and beyond from Andrew Howroyd, Nov 05 2019

Status

approved