OFFSET
1,2
COMMENTS
Number of facets of the n-th multiplihedron.
LINKS
Colin Barker, Table of n, a(n) for n = 1..1000
Stefan Forcey, Convex Hull Realizations of the Multiplihedra, arXiv:0706.3226 [math.AT], 2007-2008. See Theorem 2.4 p. 8.
Index entries for linear recurrences with constant coefficients, signature (5,-9,7,-2).
FORMULA
From Colin Barker, Jun 10 2020: (Start)
G.f.: x^2*(2 - 4*x + x^2) / ((1 - x)^3*(1 - 2*x)).
a(n) = 5*a(n-1) - 9*a(n-2) + 7*a(n-3) - 2*a(n-4) for n>4.
(End)
PROG
(PARI) a(n) = n*(n-1)/2 + 2^(n-1) - 1;
(PARI) concat(0, Vec(x^2*(2 - 4*x + x^2) / ((1 - x)^3*(1 - 2*x)) + O(x^40))) \\ Colin Barker, Jun 10 2020
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Michel Marcus, Jun 10 2020
STATUS
approved