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A357592 Number of edges of the Minkowski sum of n simplices with vertices e_(i+1), e_(i+2), e_(i+3) for i=0,...,n-1, where e_i is a standard basis vector.

%I A357592 #8 Nov 19 2022 14:08:00
%S A357592 3,11,34,96,260,683,1757,4447,11114,27493
%N A357592 Number of edges of the Minkowski sum of n simplices with vertices e_(i+1), e_(i+2), e_(i+3) for i=0,...,n-1, where e_i is a standard basis vector.
%H A357592 L. Escobar, P. Gallardo, J. González-Anaya, J. L. González, G. Montúfar, and A. H. Morales, <a href="https://arxiv.org/abs/2209.14978">Enumeration of max-pooling responses with generalized permutohedra</a>, arXiv:2209.14978 [math.CO], 2022. (See Table 2)
%o A357592 (Sage) def a(n): return len(PP(n,3,1).graph().edges())
%o A357592 def Delta(I,n):
%o A357592     IM = identity_matrix(n)
%o A357592     return Polyhedron(vertices=[IM[e] for e in I],backend='normaliz')
%o A357592 def Py(n,SL,yL):
%o A357592     return sum(yL[i]*Delta(SL[i],n) for i in range(len(SL)))
%o A357592 def PP(n,k,s):
%o A357592     SS = [set(range(s*i,k+s*i)) for i in range(n)],[1,]*(n)
%o A357592     return Py(s*(n-1)+k,SS[0],SS[1])
%o A357592 [a(n) for n in range(1,4)]
%Y A357592 Cf. A033303, A007070.
%K A357592 nonn,hard,more
%O A357592 1,1
%A A357592 _Alejandro H. Morales_, Oct 05 2022