A271509 List of 5-tuples: primitive integral pentagon sides in Cairo tiling.

5, 5, 5, 5, 2, 13, 13, 13, 13, 14, 17, 17, 17, 17, 14, 25, 25, 25, 25, 34, 29, 29, 29, 29, 2, 37, 37, 37, 37, 46, 41, 41, 41, 41, 62, 53, 53, 53, 53, 34, 61, 61, 61, 61, 98, 65, 65, 65, 65, 94, 65, 65, 65, 65, 46, 73, 73, 73, 73, 14

Offset

1,1

Comments

Refer to Cairo tiling by Stick Cross Method (see details in the links). Each pentagon has four sides of equal length and one side which is either shorter or longer. All sides can be taken to have integral lengths related to primitive Pythagorean triples A103606.

If Pythagorean triple = (a, b, c), the 5-tuple is (s1, s2, s3, s4, s5) with s1 = s2 = s3 = s4 = c and s5 = 2*(b-a). See illustration in the links.

Links

Table of n, a(n) for n=1..60.

David Bailey's World of Escher-like Tessellations, Stick Cross Method

Kival Ngaokrajang, Illustration of initial terms, Excel calculation sheet

Wikipedia, Cairo pentagonal tiling

Example

List begins:
5, 5, 5, 5, 2,
13, 13, 13, 13, 14,
17, 17, 17, 17, 14,
25, 25, 25, 25, 34,
29, 29, 29, 29, 2,
...

Crossrefs

Cf. A103606.

Sequence in context: A083945 A125563 A093704 * A269626 A269268 A112110

Adjacent sequences: A271506 A271507 A271508 * A271510 A271511 A271512

Keyword

nonn,tabf

Author

Kival Ngaokrajang, Apr 09 2016

Status

approved