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A165875 Number of reduced words of length n in Coxeter group on 15 generators S_i with relations (S_i)^2 = (S_i S_j)^10 = I. 1
1, 15, 210, 2940, 41160, 576240, 8067360, 112943040, 1581202560, 22136835840, 309915701655, 4338819821700, 60743477483325, 850408684479900, 11905721578705500, 166680102045693600, 2333521427853142800 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

The initial terms coincide with those of A170734, 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 (13,13,13,13,13,13,13,13,13,-91).

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)/(91*t^10 - 13*t^9 - 13*t^8 - 13*t^7 - 13*t^6 - 13*t^5 - 13*t^4 - 13*t^3 - 13*t^2 - 13*t + 1).

MAPLE

seq(coeff(series((1+t)*(1-t^10)/(1-14*t+104*t^10-91*t^11), t, n+1), t, n), n = 0..20); # G. C. Greubel, Sept 23 2019

MATHEMATICA

CoefficientList[Series[(1+t)*(1-t^10)/(1-14*t+104*t^10-91*t^11), {t, 0, 25}], t] (* G. C. Greubel, Apr 17 2016 *)

coxG[{10, 91, -13}] (* The coxG program is at A169452 *) (* G. C. Greubel, Sep 23 2019 *)

PROG

(PARI) my(t='t+O('t^30)); Vec((1+t)*(1-t^10)/(1-14*t+104*t^10-91*t^11)) \\ G. C. Greubel, Sep 23 2019

(MAGMA) R<t>:=PowerSeriesRing(Integers(), 30); Coefficients(R!( (1+t)*(1-t^10)/(1-14*t+104*t^10-91*t^11) )); // G. C. Greubel, Sep 23 2019

(Sage)

def A165875_list(prec):

    P.<t> = PowerSeriesRing(ZZ, prec)

    return P((1+t)*(1-t^10)/(1-14*t+104*t^10-91*t^11)).list()

A165875_list(30) # G. C. Greubel, Sep 23 2019

(GAP) a:=[15, 210, 2940, 41160, 576240, 8067360, 112943040, 1581202560, 22136835840, 309915701655];; for n in [11..20] do a[n]:=13*Sum([1..9], j-> a[n-j]) -19*a[n-10]; od; Concatenation([1], a); # G. C. Greubel, Sep 23 2019

CROSSREFS

Sequence in context: A164626 A164860 A165282 * A166382 A166583 A166971

Adjacent sequences:  A165872 A165873 A165874 * A165876 A165877 A165878

KEYWORD

nonn

AUTHOR

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

STATUS

approved

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Last modified November 22 10:59 EST 2019. Contains 329389 sequences. (Running on oeis4.)