OFFSET
1,2
COMMENTS
Proved via a combinatorial argument.
LINKS
Henry L. Fleischmann et al., Distinct Angle Problems and Variants, arXiv:2108.12015 [math.CO], 2021.
Index entries for linear recurrences with constant coefficients, signature (11,-31,21).
FORMULA
a(n) = (7^n - 3^(n+1) + 2)/12.
a(n) = 2*A016212(n-2) for n >= 2.
G.f.: 2*x^2/(1 - 11*x + 31*x^2 - 21*x^3). - Stefano Spezia, Aug 04 2021
EXAMPLE
The 1-dimensional hypercube (vertices 0 and 1 on a line) has no triangles and thus no classes of triangle equivalent up to edge translation, so a(1)=0.
A square, the 2-dimensional hypercube, has two distinct right triangles up to edge translation, so a(2)=2.
PROG
(Python) def a(n): return (7**n - 3**(n+1) + 2)//12
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Henry L. Fleischmann, Aug 04 2021
STATUS
approved