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.

3, 11, 34, 96, 260, 683, 1757, 4447, 11114, 27493

Offset

1,1

Links

Table of n, a(n) for n=1..10.

L. Escobar, P. Gallardo, J. González-Anaya, J. L. González, G. Montúfar, and A. H. Morales, Enumeration of max-pooling responses with generalized permutohedra, arXiv:2209.14978 [math.CO], 2022. (See Table 2)

Prog

(Sage) def a(n): return len(PP(n, 3, 1).graph().edges())
def Delta(I, n):
    IM = identity_matrix(n)
    return Polyhedron(vertices=[IM[e] for e in I], backend='normaliz')
def Py(n, SL, yL):
    return sum(yL[i]*Delta(SL[i], n) for i in range(len(SL)))
def PP(n, k, s):
    SS = [set(range(s*i, k+s*i)) for i in range(n)], [1, ]*(n)
    return Py(s*(n-1)+k, SS[0], SS[1])
[a(n) for n in range(1, 4)]

Crossrefs

Cf. A033303, A007070.

Sequence in context: A247103 A036542 A084266 * A052471 A037496 A355364

Adjacent sequences: A357589 A357590 A357591 * A357593 A357594 A357595

Keyword

nonn,hard,more

Author

Alejandro H. Morales, Oct 05 2022

Status

approved