A261681 a(n) = 2^n + binomial(n, floor(n/2)) - 1.

1, 2, 5, 10, 21, 41, 83, 162, 325, 637, 1275, 2509, 5019, 9907, 19815, 39202, 78405, 155381, 310763, 616665, 1233331, 2449867, 4899735, 9740685, 19481371, 38754731, 77509463, 154276027, 308552055, 614429671, 1228859343, 2448023842, 4896047685, 9756737701

Offset: 0

Author

N. J. A. Sloane, Sep 04 2015

Keywords

• nonn

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.

Crossrefs

Cf. A000079, A014495.

Cf. A000225, A001405.

Programs

Magma

[2^n+Binomial(n, Floor(n/2))-1: n in [0..40]]; // Vincenzo Librandi, Sep 05 2015

Mathematica

Table[2^n + Binomial[n, Floor[n/2]] - 1, {n, 0, 40}] (* Vincenzo Librandi, Sep 05 2015 *)

PARI

a(n) = 2^n + binomial(n, n\2) - 1 \\ Michel Marcus, Sep 05 2015

Formula

a(n) = A000079(n) + A014495(n).

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