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A165980 Number of reduced words of length n in Coxeter group on 28 generators S_i with relations (S_i)^2 = (S_i S_j)^10 = I. 1
1, 28, 756, 20412, 551124, 14880348, 401769396, 10847773692, 292889889684, 7908027021468, 213516729579258, 5764951698629760, 155653695862728336, 4202649788286235104, 113471544283527738672, 3063731695649832497472 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

The initial terms coincide with those of A170747, 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 (26,26,26,26,26,26,26,26,26,-351).

FORMULA

G.f.: (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)/(351*t^10 - 26*t^9 - 26*t^8 - 26*t^7 - 26*t^6 - 26*t^5 - 26*t^4 - 26*t^3 - 26*t^2 - 26*t + 1).

MAPLE

seq(coeff(series((1+t)*(1-t^10)/(1-27*t+377*t^10-351*t^11), t, n+1), t, n), n = 0..30); # G. C. Greubel, Oct 25 2019

MATHEMATICA

CoefficientList[Series[(1+t)*(1-t^10)/(1-27*t+377*t^10-351*t^11), {t, 0, 30}], t] (* G. C. Greubel, Apr 20 2016 *)

coxG[{10, 351, -26}] (* The coxG program is at A169452 *) (* G. C. Greubel, Oct 25 2019 *)

PROG

(PARI) my(t='t+O('t^30)); Vec((1+t)*(1-t^10)/(1-27*t+377*t^10-351*t^11)) \\ G. C. Greubel, Oct 25 2019

(MAGMA) R<t>:=PowerSeriesRing(Integers(), 30); Coefficients(R!( (1+t)*(1-t^10)/(1-27*t+377*t^10-351*t^11) )); // G. C. Greubel, Oct 25 2019

(Sage)

def A165980_list(prec):

    P.<t> = PowerSeriesRing(ZZ, prec)

    return P((1+t)*(1-t^10)/(1-27*t+377*t^10-351*t^11)).list()

A165980_list(30) # G. C. Greubel, Oct 25 2019

(GAP) a:=[28, 756, 20412, 551124, 14880348, 401769396, 10847773692, 292889889684, 7908027021468, 213516729579258];; for n in [11..30] do a[n]:=26*Sum([1..9], j-> a[n-j]) - 351*a[n-10]; od; Concatenation([1], a); # G. C. Greubel, Oct 25 2019

CROSSREFS

Sequence in context: A164664 A164970 A165456 * A166422 A166615 A167081

Adjacent sequences:  A165977 A165978 A165979 * A165981 A165982 A165983

KEYWORD

nonn

AUTHOR

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

STATUS

approved

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Last modified April 22 11:08 EDT 2021. Contains 343174 sequences. (Running on oeis4.)