OFFSET
3,1
COMMENTS
a(n) is also the number of partitions of (n-2)*180 into n parts.
REFERENCES
G. E. Andrews, The Theory of Partitions, Addison-Wesley (1976), pp. 56-57 (Chapter 4).
LINKS
Alois P. Heinz, Table of n, a(n) for n = 3..444
Felix Huber, Example 3-gon
Wikipedia, Partition
Wikipedia, Polygon
FORMULA
a(n) = A008284((n-2)*180,n). - Alois P. Heinz, Aug 08 2023
EXAMPLE
For n = 3 the a(3) = 2700 sets of integer angles {u, v, w} are in links "Example 3-gon".
MAPLE
b:= proc(n, i) option remember; `if`(min(n, i)<0, 0,
`if`(i=0, `if`(n=0, 1, 0), b(n-1, i-1)+b(n-i, i)))
end:
a:= n-> b((n-2)*180, n):
seq(a(n), n=3..25); # Alois P. Heinz, Aug 08 2023
MATHEMATICA
b[n_, i_] := b[n, i] = If[Min[n, i] < 0, 0, If[i == 0, If[n == 0, 1, 0], b[n-1, i-1] + b[n-i, i]]];
a[n_] := b[(n-2)*180, n];
Table[a[n], {n, 3, 25}] (* Jean-François Alcover, Nov 08 2023, after Alois P. Heinz *)
PROG
(PARI) a(n)={my(m=179*n-360); polcoef(1/prod(k=1, n, 1-x^k + O(x*x^m)), m)} \\ Andrew Howroyd, Aug 08 2023
CROSSREFS
KEYWORD
nonn
AUTHOR
Felix Huber, Aug 08 2023
EXTENSIONS
a(7)-a(16) from Alois P. Heinz, Aug 08 2023
STATUS
approved