A098912 Number of ways angles from Pi/n to (n-1)Pi/n can tile around a vertex, where rotations and reflections of an angle sequence are not counted.
1, 5, 16, 54, 180, 607, 2098, 7397, 26452, 95821, 350554, 1292634, 4797694, 17904220, 67125898, 252679320, 954505718, 3616951513, 13744169104, 52358244166, 199912298266, 764879838343, 2932035371786, 11259007784430, 43303859981236, 166800020984581
Offset: 2
Keywords
Examples
a(3) = 5 because we can write 2pi = 2'+2'+2' or 2'+1'+2'+1' or 2'+2'+1'+1' or 2'+1'+1'+1'+1' or 1'+1'+1'+1'+1'+1' where k' = k pi/3.
Links
- Andrew Howroyd, Table of n, a(n) for n = 2..200
Programs
-
Mathematica
b[n_] := (1/n)*DivisorSum[n, EulerPhi[n/#] * 2^# &]; a[n_] := b[2*n]/2 + 2^(n-2) - 2^Quotient[n, 2] - 2^Quotient[n-1, 2]; Table[a[n], {n, 2, 27}] (* Jean-François Alcover, Oct 08 2017, translated from PARI *) -
PARI
b(n) = (1/n)*sumdiv(n, d, eulerphi(n/d) * 2^d); a(n) = b(2*n)/2 + 2^(n-2) - 2^(n\2) - 2^((n-1)\2); \\ Andrew Howroyd, Sep 06 2017
Formula
From Andrew Howroyd, Sep 06 2017: (Start)
a(n) = 2^(n-2) - 2^(floor(n/2)) - 2^(floor((n-1)/2)) + (1/(4*n)) * (Sum_{d | 2*n} phi(2*n/d) * 2^d).
(End)
Extensions
Terms a(8) and beyond from Andrew Howroyd, Sep 06 2017
Comments