|
%I #20 Sep 08 2022 08:46:13
%S 1,2,5,10,21,41,83,162,325,637,1275,2509,5019,9907,19815,39202,78405,
%T 155381,310763,616665,1233331,2449867,4899735,9740685,19481371,
%U 38754731,77509463,154276027,308552055,614429671,1228859343,2448023842,4896047685,9756737701
%N a(n) = 2^n + binomial(n, floor(n/2)) - 1.
%H Riccardo Biagioli, Frédéric Jouhet, and Philippe Nadeau, <a href="http://arxiv.org/abs/1411.4561">Combinatorics of fully commutative involutions in classical Coxeter groups</a>, arXiv preprint arXiv:1411.4561 [math.CO] (2014). See Prop. 2.1.
%H Riccardo Biagioli, Frédéric Jouhet, and Philippe Nadeau, <a href="http://dx.doi.org/10.1016/j.disc.2015.05.023">Combinatorics of fully commutative involutions in classical Coxeter groups</a>, Discrete Math., 338 (2015), 2242-2259. See Prop. 2.1.
%F a(n) = A000079(n) + A014495(n).
%F Conjecture: -(n+1)*(n-4)*a(n) +(3*n^2-9*n-8)*a(n-1) +2*(n^2-9*n+16)*a(n-2) +4*(-3*n^2+18*n-25)*a(n-3) +8*(n-3)^2*a(n-4)=0. - _R. J. Mathar_, Jan 04 2017
%F a(n) = Sum_{i=1..n+1} C(n,floor(i/2)). - _Wesley Ivan Hurt_, Nov 22 2017
%t Table[2^n + Binomial[n, Floor[n/2]] - 1, {n, 0, 40}] (* _Vincenzo Librandi_, Sep 05 2015 *)
%o (PARI) a(n) = 2^n + binomial(n, n\2) - 1 \\ _Michel Marcus_, Sep 05 2015
%o (Magma) [2^n+Binomial(n, Floor(n/2))-1: n in [0..40]]; // _Vincenzo Librandi_, Sep 05 2015
%Y Cf. A000079, A014495.
%Y Cf. A000225, A001405.
%K nonn
%O 0,2
%A _N. J. A. Sloane_, Sep 04 2015
|
