A013981 Number of commutative elements in Coxeter group H_n.

1, 2, 9, 44, 195, 804, 3185, 12368, 47607, 182720, 701349, 2695978, 10384231, 40083848, 155052001, 600949336, 2333344095, 9074611032, 35344215245, 137844431690, 538253680159, 2104090575136, 8233413950409

Offset

0,2

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=0..22.

Boothby, T.; Burkert, J.; Eichwald, M.; Ernst, D. C.; Green, R. M.; Macauley, M.  On the cyclically fully commutative elements of Coxeter groups, J. Algebr. Comb. 36, No. 1, 123-148 (2012), Table 1 type H.

Formula

a(n) = A000984(n) -2^(n+2) +n+3.

-finite: -(n+1)*(131*n-245) *a(n) +2*(563*n^2-867*n-245) *a(n-1) +3*(-1099*n^2+2480*n-1105) *a(n-2) +2*(1987*n^2-5829*n+4205) *a(n-3) -4*(209*n-178)*(2*n-5) *a(n-4)=0. - R. J. Mathar, Jun 11 2019

Maple

seq( binomial(2*n+2, n+1)-2^(n+2)+n+3, n=0..20);

Crossrefs

Sequence in context: A163650 A259777 A365038 * A216861 A199308 A176479

Adjacent sequences: A013978 A013979 A013980 * A013982 A013983 A013984

Keyword

nonn,easy

Author

Ken Fan

Status

approved