cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

A346796 Number of equivalence classes of triangles in an n-dimensional hypercube, equivalent up to translation of difference vectors corresponding to edges.

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%I A346796 #30 Aug 30 2021 05:34:39
%S A346796 0,2,22,180,1340,9622,68082,478760,3357880,23524842,164732942,
%T A346796 1153307740,8073685620,56517393662,395626538602,2769400119120,
%U A346796 19385843880560,135701036304082,949907641549062,6649354653104900
%N A346796 Number of equivalence classes of triangles in an n-dimensional hypercube, equivalent up to translation of difference vectors corresponding to edges.
%C A346796 Proved via a combinatorial argument.
%H A346796 Henry L. Fleischmann et al., <a href="https://arxiv.org/abs/2108.12015">Distinct Angle Problems and Variants</a>, arXiv:2108.12015 [math.CO], 2021.
%H A346796 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (11,-31,21).
%F A346796 a(n) = (7^n - 3^(n+1) + 2)/12.
%F A346796 a(n) = 2*A016212(n-2) for n >= 2.
%F A346796 G.f.: 2*x^2/(1 - 11*x + 31*x^2 - 21*x^3). - _Stefano Spezia_, Aug 04 2021
%e A346796 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.
%e A346796 A square, the 2-dimensional hypercube, has two distinct right triangles up to edge translation, so a(2)=2.
%o A346796 (Python) def a(n): return (7**n - 3**(n+1) + 2)//12
%Y A346796 Cf. A016212 (allowing flips as well as edge translations, up to offset).
%K A346796 nonn,easy
%O A346796 1,2
%A A346796 _Henry L. Fleischmann_, Aug 04 2021