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A346796
Number of equivalence classes of triangles in an n-dimensional hypercube, equivalent up to translation of difference vectors corresponding to edges.
0
0, 2, 22, 180, 1340, 9622, 68082, 478760, 3357880, 23524842, 164732942, 1153307740, 8073685620, 56517393662, 395626538602, 2769400119120, 19385843880560, 135701036304082, 949907641549062, 6649354653104900
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.
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
Cf. A016212 (allowing flips as well as edge translations, up to offset).
Sequence in context: A270407 A000184 A007613 * A279801 A043037 A058441
KEYWORD
nonn,easy
AUTHOR
STATUS
approved