A335439 a(n) = n*(n-1)/2 + 2^(n-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

Author

Michel Marcus, Jun 10 2020

Keywords

• nonn
• easy

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).

Crossrefs

Cf. A000217, A000225, A121988 (number of vertices of the n-th multiplihedron).

Programs

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

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)