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A335439
a(n) = n*(n-1)/2 + 2^(n-1) - 1.
1
0, 2, 6, 13, 25, 46, 84, 155, 291, 556, 1078, 2113, 4173, 8282, 16488, 32887, 65671, 131224, 262314, 524477, 1048785, 2097382, 4194556, 8388883, 16777515, 33554756, 67109214, 134218105, 268435861, 536871346, 1073742288, 2147484143, 4294967823, 8589935152, 17179869778
OFFSET
1,2
COMMENTS
Number of facets of the n-th multiplihedron.
LINKS
Stefan Forcey, Convex Hull Realizations of the Multiplihedra, arXiv:0706.3226 [math.AT], 2007-2008. See Theorem 2.4 p. 8.
FORMULA
a(n) = A000217(n-1) + A000225(n-1).
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
Cf. A000217, A000225, A121988 (number of vertices of the n-th multiplihedron).
Sequence in context: A267698 A065220 A048094 * A181522 A031872 A259577
KEYWORD
nonn,easy
AUTHOR
Michel Marcus, Jun 10 2020
STATUS
approved