A013980 Number of commutative elements in Coxeter group F_n.

24, 106, 464, 2003, 8560, 36333, 153584, 647775, 2729365, 11496788, 48433965, 204115805, 860593940, 3630164290, 15319869152, 64680076487, 273183844396, 1154223866418, 4878180558021, 20622538937234, 87202351145432, 368810395465291

Offset

3,1

References

C. Kenneth Fan, Structure of a Hecke algebra quotient. J. Amer. Math. Soc. 10 (1997), no. 1, 139-167.

C. K. Fan, A Hecke algebra quotient and some combinatorial applications. J. Algebraic Combin. 5 (1996), no. 3, 175-189.

Links

Table of n, a(n) for n=3..24.

John R. Stembridge, The Enumeration of Fully Commutative Elements of Coxeter Groups, Dept. of Mathematics, Uni. of Michigan, 1996.

Formula

From Sean A. Irvine, Sep 07 2018: (Start)

G.f.: (10 - 5 * (1+x) * (C(x)-1)) / (1-4*x-x^2) + (R(x)-1) / x - (6-4*x) / (1-3*x+x^2) + (1+x) / (1-x-x^2) - 1 / (1-x) where C(x) = (1 - sqrt(1-4*x)) / (2*x) is the g.f. for the Catalan numbers [From Stembridge].

a(n) = C(n-1) + 5 * F(3*n-3) - 2 * F(2*n-1) - 2 * F(2*n-3) + F(n) - 1 - 5 * Sum_{k=2..n-1} F(3*k-4) * C(n-k) where C(n) = A000108(n) are the Catalan numbers and F(n) = A000045(n) are the Fibonacci numbers. (End)

Crossrefs

Cf. A000045, A000108.

Sequence in context: A011199 A213874 A100149 * A100150 A305950 A060334

Adjacent sequences: A013977 A013978 A013979 * A013981 A013982 A013983

Keyword

nonn

Author

Ken Fan

Extensions

More terms from Sean A. Irvine, Sep 07 2018

Status

approved