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A013981 Number of commutative elements in Coxeter group H_n. 0
1, 2, 9, 44, 195, 804, 3185, 12368, 47607, 182720, 701349, 2695978, 10384231, 40083848, 155052001, 600949336, 2333344095, 9074611032, 35344215245, 137844431690, 538253680159, 2104090575136, 8233413950409 (list; graph; refs; listen; history; text; internal format)
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: A294270 A163650 A259777 * A216861 A199308 A176479

Adjacent sequences:  A013978 A013979 A013980 * A013982 A013983 A013984

KEYWORD

nonn,easy

AUTHOR

Ken Fan

STATUS

approved

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Last modified June 15 15:16 EDT 2021. Contains 345049 sequences. (Running on oeis4.)