A167681 Number of reduced words of length n in Coxeter group on 21 generators S_i with relations (S_i)^2 = (S_i S_j)^15 = I.

1, 21, 420, 8400, 168000, 3360000, 67200000, 1344000000, 26880000000, 537600000000, 10752000000000, 215040000000000, 4300800000000000, 86016000000000000, 1720320000000000000, 34406399999999999790

Offset

0,2

Comments

The initial terms coincide with those of A170740, although the two sequences are eventually different.

Computed with Magma using commands similar to those used to compute A154638.

Links

G. C. Greubel, Table of n, a(n) for n = 0..500

Index entries for linear recurrences with constant coefficients, signature (19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, -190).

Formula

G.f.: (t^15 + 2*t^14 + 2*t^13 + 2*t^12 + 2*t^11 + 2*t^10 + 2*t^9 + 2*t^8 + 2*t^7 + 2*t^6 + 2*t^5 + 2*t^4 + 2*t^3 + 2*t^2 + 2*t + 1)/(190*t^15 - 19*t^14 - 19*t^13 - 19*t^12 - 19*t^11 - 19*t^10 - 19*t^9 - 19*t^8 - 19*t^7 - 19*t^6 - 19*t^5 - 19*t^4 - 19*t^3 - 19*t^2 - 19*t + 1).

Mathematica

CoefficientList[Series[(t^15 + 2*t^14 + 2*t^13 + 2*t^12 + 2*t^11 + 2*t^10 + 2*t^9 + 2*t^8 + 2*t^7 + 2*t^6 + 2*t^5 + 2*t^4 + 2*t^3 + 2*t^2 + 2*t + 1)/(190*t^15 - 19*t^14 - 19*t^13 - 19*t^12 - 19*t^11 - 19*t^10 - 19*t^9 - 19*t^8 - 19*t^7 - 19*t^6 - 19*t^5 - 19*t^4 - 19*t^3 - 19*t^2 - 19*t + 1), {t, 0, 50}], t] (* G. C. Greubel, Jun 19 2016 *)

Prog

(PARI) first(n)=Vec((1+x^5+x^10)*(1+x+x^2+x^3+x^4)*(1+x)/(1-19*x-19*x^2-19*x^3-19*x^4-19*x^5-19*x^6-19*x^7-19*x^8-19*x^9-19*x^10-19*x^11-19*x^12-19*x^13-19*x^14+190*x^15)+O(x^(n+1))) \\ Charles R Greathouse IV, Jun 12 2026

Crossrefs

Cf. A170740, A154638.

Sequence in context: A166603 A167074 A167150 * A167933 A168698 A168746

Adjacent sequences: A167678 A167679 A167680 * A167682 A167683 A167684

Keyword

nonn,easy

Author

John Cannon and N. J. A. Sloane, Dec 03 2009

Status

approved