A098913 Number of different ways angles from Pi/n to (n-1)Pi/n can tile around a vertex, where rotations of an angle sequence are not counted, but reflections that are different are counted.
1, 5, 19, 75, 287, 1053, 3859, 14089, 51463, 188697, 695155, 2573235, 9571195, 35759799, 134154259, 505163055, 1908619755, 7233118641, 27486768415, 104713346699, 399818311219, 1529747101965, 5864045590035, 22517965253595, 86607619323751, 333599840675337
Offset: 2
Keywords
Examples
a(4)=19 because 2pi = 3'3'2' or 2'2'2'2' or 3'1'2'2' or 3'1'3'1' or 3'2'1'2' or 3'2'2'1' or 3'3'1'1' or 2'2'1'2'1' or 2'2'2'1'1' or 3'1'1'1'2' or 3'1'1'2'1' or 3'1'2'1'1' or 3'2'1'1'1' or 2'1'1'2'1'1' or 2'1'2'1'1'1' or 2'2'1'1'1'1' or 3'1'1'1'1'1' or 2'1'1'1'1'1'1' or 1'1'1'1'1'1'1'1' where k' = k pi/4. Note 3'2'2'1 and 3'1'2'2'; 3'1'1'2'1' and 3'1'2'1'1'; 3'1'1'1'2' and 3'2'1'1'1' are different by rotation but not reflection
Links
- Andrew Howroyd, Table of n, a(n) for n = 2..200
Programs
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PARI
b(n) = (1/n)*sumdiv(n, d, eulerphi(n/d) * 2^d); a(n) = b(2*n) - 1 - 2^n; \\ Andrew Howroyd, Sep 06 2017
Formula
From Andrew Howroyd, Sep 06 2017: (Start)
a(n) = A008965(2*n) - 2^n.
a(n) = (Sum_{d | 2*n} phi(2*n/d) * 2^d)/(2*n) - 1 - 2^n.
(End)
Extensions
Terms a(8) and beyond from Andrew Howroyd, Sep 06 2017
Comments