A167075 - OEIS

A167075

Number of reduced words of length n in Coxeter group on 22 generators S_i with relations (S_i)^2 = (S_i S_j)^13 = I.

1, 22, 462, 9702, 203742, 4278582, 89850222, 1886854662, 39623947902, 832102905942, 17474161024782, 366957381520422, 7706105011928862, 161828205250505871, 3398392310260618440, 71366238515472885600

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OFFSET

0,2

COMMENTS

The initial terms coincide with those of A170741, 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 (20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, -210).

FORMULA

G.f.: (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)/(210*t^13 - 20*t^12 - 20*t^11 - 20*t^10 - 20*t^9 - 20*t^8 - 20*t^7 - 20*t^6 - 20*t^5 - 20*t^4 - 20*t^3 - 20*t^2 - 20*t + 1).

MATHEMATICA

CoefficientList[Series[(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)/(210*t^13 - 20*t^12 - 20*t^11 - 20*t^10 - 20*t^9 - 20*t^8 - 20*t^7 - 20*t^6 - 20*t^5 - 20*t^4 - 20*t^3 - 20*t^2 - 20*t + 1), {t, 0, 50}], t] (* G. C. Greubel, May 31 2016 *)

coxG[{13, 210, -20}] (* The coxG program is at A169452 *) (* Harvey P. Dale, Dec 10 2017 *)

PROG

(PARI) Vec((1+x+x^2+x^3+x^4+x^5+x^6+x^7+x^8+x^9+x^10+x^11+x^12)*(1+x)/(1-20*x-20*x^2-20*x^3-20*x^4-20*x^5-20*x^6-20*x^7-20*x^8-20*x^9-20*x^10-20*x^11-20*x^12+210*x^13)+O(x^99)) \\ Charles R Greathouse IV, Jun 08 2026

CROSSREFS

Cf. A170741, A154638.

Sequence in context: A165895 A166416 A166608 * A167173 A167693 A167935

Adjacent sequences: A167072 A167073 A167074 * A167076 A167077 A167078

KEYWORD

nonn,easy

AUTHOR

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

STATUS

approved