OFFSET
0,2
LINKS
Riccardo Biagioli, Frédéric Jouhet, and Philippe Nadeau, Combinatorics of fully commutative involutions in classical Coxeter groups, arXiv preprint arXiv:1411.4561 [math.CO] (2014). See Prop. 2.1.
Riccardo Biagioli, Frédéric Jouhet, and Philippe Nadeau, Combinatorics of fully commutative involutions in classical Coxeter groups, Discrete Math., 338 (2015), 2242-2259. See Prop. 2.1.
FORMULA
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
a(n) = Sum_{i=1..n+1} C(n,floor(i/2)). - Wesley Ivan Hurt, Nov 22 2017
MATHEMATICA
Table[2^n + Binomial[n, Floor[n/2]] - 1, {n, 0, 40}] (* Vincenzo Librandi, Sep 05 2015 *)
PROG
(PARI) a(n) = 2^n + binomial(n, n\2) - 1 \\ Michel Marcus, Sep 05 2015
(Magma) [2^n+Binomial(n, Floor(n/2))-1: n in [0..40]]; // Vincenzo Librandi, Sep 05 2015
CROSSREFS
KEYWORD
nonn
AUTHOR
N. J. A. Sloane, Sep 04 2015
STATUS
approved