%I #10 Sep 24 2025 10:19:58

%S 0,1,6,8,18,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,

%T 8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,

%U 8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8

%N Number of regular (infinite) apeirotopes of full rank in n-dimensional space.

%D Peter McMullen, Regular polytopes of full rank, lecture at The Coxeter Legacy meeting, Toronto, 2004.

%D Peter McMullen and Egon Schulte, Abstract Regular Polytopes, Encyclopedia of Mathematics and its Applications, Vol. 92, Cambridge University Press, Cambridge, 2002.

%D Peter McMullen and Egon Schulte, Paper to appear in Discrete and Computational Geometry, 2004.

%H Peter McMullen, <a href="https://doi.org/10.1007/s00454-004-0848-5">Regular polytopes of full rank</a>, Discrete Comput Geom 32, 1-35 (2004). See p. 34.

%H <a href="/index/Rec#order_01">Index entries for linear recurrences with constant coefficients</a>, signature (1).

%F From _Elmo R. Oliveira_, Sep 23 2025: (Start)

%F G.f.: x*(1 + 5*x + 2*x^2 + 10*x^3 - 10*x^4)/(1 - x).

%F E.g.f.: 8*(exp(x) - 1) - 7*x - x^2 + 5*x^4/12.

%F a(n) = 8 for n > 4. (End)

%Y Cf. A093478, A060296, A000943, A000944, A053016, A063927.

%K nonn,easy

%O 0,3

%A _N. J. A. Sloane_, May 22 2004