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A271509 List of 5-tuples: primitive integral pentagon sides in Cairo tiling. 1

%I

%S 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,

%T 37,37,37,37,46,41,41,41,41,62,53,53,53,53,34,61,61,61,61,98,65,65,65,

%U 65,94,65,65,65,65,46,73,73,73,73,14

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

%C 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.

%C 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.

%H David Bailey's World of Escher-like Tessellations, <a href="http://www.tess-elation.co.uk/cairo-tiling/study-1">Stick Cross Method</a>

%H Kival Ngaokrajang, <a href="/A271509/a271509.pdf">Illustration of initial terms</a>, <a href="/A271509/a271509_1.pdf">Excel calculation sheet</a>

%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Cairo_pentagonal_tiling">Cairo pentagonal tiling</a>

%e List begins:

%e 5, 5, 5, 5, 2,

%e 13, 13, 13, 13, 14,

%e 17, 17, 17, 17, 14,

%e 25, 25, 25, 25, 34,

%e 29, 29, 29, 29, 2,

%e ...

%Y Cf. A103606.

%K nonn,tabf

%O 1,1

%A _Kival Ngaokrajang_, Apr 09 2016

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Last modified October 20 07:17 EDT 2018. Contains 316378 sequences. (Running on oeis4.)