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

%I A335439 #12 Jun 11 2020 02:31:57
%S A335439 0,2,6,13,25,46,84,155,291,556,1078,2113,4173,8282,16488,32887,65671,
%T A335439 131224,262314,524477,1048785,2097382,4194556,8388883,16777515,
%U A335439 33554756,67109214,134218105,268435861,536871346,1073742288,2147484143,4294967823,8589935152,17179869778
%N A335439 a(n) = n*(n-1)/2 + 2^(n-1) - 1.
%C A335439 Number of facets of the n-th multiplihedron.
%H A335439 Colin Barker, <a href="/A335439/b335439.txt">Table of n, a(n) for n = 1..1000</a>
%H A335439 Stefan Forcey, <a href="https://arxiv.org/abs/0706.3226">Convex Hull Realizations of the Multiplihedra</a>, arXiv:0706.3226 [math.AT], 2007-2008. See Theorem 2.4 p. 8.
%H A335439 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (5,-9,7,-2).
%F A335439 a(n) = A000217(n-1) + A000225(n-1).
%F A335439 From _Colin Barker_, Jun 10 2020: (Start)
%F A335439 G.f.: x^2*(2 - 4*x + x^2) / ((1 - x)^3*(1 - 2*x)).
%F A335439 a(n) = 5*a(n-1) - 9*a(n-2) + 7*a(n-3) - 2*a(n-4) for n>4.
%F A335439 (End)
%o A335439 (PARI) a(n) = n*(n-1)/2 + 2^(n-1) - 1;
%o A335439 (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
%Y A335439 Cf. A000217, A000225, A121988 (number of vertices of the n-th multiplihedron).
%K A335439 nonn,easy
%O A335439 1,2
%A A335439 _Michel Marcus_, Jun 10 2020