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A165967 Number of reduced words of length n in Coxeter group on 25 generators S_i with relations (S_i)^2 = (S_i S_j)^10 = I. 1
1, 25, 600, 14400, 345600, 8294400, 199065600, 4777574400, 114661785600, 2751882854400, 66045188505300, 1585084524120000, 38042028578707500, 913008685884840000, 21912208461136800000, 525893003064898560000 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

The initial terms coincide with those of A170744, 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 (23,23,23,23,23,23,23,23,23,-276).

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)/(276*t^10 - 23*t^9 - 23*t^8 - 23*t^7 - 23*t^6 - 23*t^5 - 23*t^4 - 23*t^3 - 23*t^2 - 23*t + 1).

MAPLE

seq(coeff(series((1+t)*(1-t^10)/(1-24*t+299*t^10-276*t^11), t, n+1), t, n), n = 0..30); # G. C. Greubel, Sep 26 2019

MATHEMATICA

CoefficientList[Series[(1+t)*(1-t^10)/(1-24*t+299*t^10-276*t^11), {t, 0, 25}], t] (* G. C. Greubel, Apr 18 2016 *)

coxG[{10, 276, -23}] (* The coxG program is at A169452 *) (* G. C. Greubel, Sep 26 2019 *)

PROG

(PARI) my(t='t+O('t^30)); Vec((1+t)*(1-t^10)/(1-24*t+299*t^10-276*t^11)) \\ G. C. Greubel, Sep 26 2019

(MAGMA) R<t>:=PowerSeriesRing(Integers(), 30); Coefficients(R!( (1+t)*(1-t^10)/(1-24*t+299*t^10-276*t^11) )); // G. C. Greubel, Sep 26 2019

(Sage)

def A165967_list(prec):

    P.<t> = PowerSeriesRing(ZZ, prec)

    return P((1+t)*(1-t^10)/(1-24*t+299*t^10-276*t^11)).list()

A165967_list(30) # G. C. Greubel, Sep 26 2019

(GAP) a:=[25, 600, 14400, 345600, 8294400, 199065600, 4777574400, 114661785600, 2751882854400, 66045188505300];; for n in [11..30] do a[n]:=23*Sum([1..9], j-> a[n-j]) -276*a[n-10]; od; Concatenation([1], a); # G. C. Greubel, Sep 26 2019

CROSSREFS

Sequence in context: A164638 A164963 A165368 * A166419 A166612 A167078

Adjacent sequences:  A165964 A165965 A165966 * A165968 A165969 A165970

KEYWORD

nonn

AUTHOR

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

STATUS

approved

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Last modified July 12 21:31 EDT 2020. Contains 335669 sequences. (Running on oeis4.)