A364795 a(n) is the number of different sets of integer angles (in degrees) of an n-gon.

2700, 326700, 30072240, 2310019204, 153386909107, 8992986080669, 472639425224952, 22527596153829699, 982894927341908652, 39558851030444690174, 1478190132737137934278, 51565891712505592101318, 1687373867784860474568905, 52009861116025253683005899

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

Cf. A000041, A008284, A008289, A066164, A000096 (second comment).

Sequence in context: A253814 A054561 A230752 * A246888 A153513 A333130

Adjacent sequences: A364792 A364793 A364794 * A364796 A364797 A364798

Keyword

nonn

Author

Felix Huber, Aug 08 2023

Extensions

a(7)-a(16) from Alois P. Heinz, Aug 08 2023

Status

approved