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A165756 Number of reduced words of length n in Coxeter group on 4 generators S_i with relations (S_i)^2 = (S_i S_j)^10 = I. 1
1, 4, 12, 36, 108, 324, 972, 2916, 8748, 26244, 78726, 236160, 708432, 2125152, 6375024, 19123776, 57367440, 172090656, 516236976, 1548605952, 4645502958, 13935564252, 41803859076, 125403076764, 376183730628, 1128474698076 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

The initial terms coincide with those of A003946, 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 (2,2,2,2,2,2,2,2,2,-3).

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)/(3*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).

MAPLE

seq(coeff(series((1+t)*(1-t^10)/(1-3*t+5*t^10-3*t^11), t, n+1), t, n), n = 0 .. 30); # G. C. Greubel, Sep 16 2019

MATHEMATICA

CoefficientList[Series[(1+t)*(1-t^10)/(1-3*t+5*t^10-3*t^11), {t, 0, 30}], t] (* G. C. Greubel, Apr 07 2016 *)

coxG[{10, 3, -2}] (* The coxG program is at A169452 *) (* G. C. Greubel, Sep 16 2019 *)

PROG

(PARI) my(t='t+O('t^30)); Vec((1+t)*(1-t^10)/(1-3*t+5*t^10-3*t^11)) \\ G. C. Greubel, Sep 16 2019

(MAGMA) R<t>:=PowerSeriesRing(Integers(), 30); Coefficients(R!( (1+t)*(1-t^10)/(1-3*t+5*t^10-3*t^11) )); // G. C. Greubel, Sep 16 2019

(Sage)

def A165756_list(prec):

    P.<t> = PowerSeriesRing(ZZ, prec)

    return P((1+t)*(1-t^10)/(1-3*t+5*t^10-3*t^11)).list()

A165756_list(30) # G. C. Greubel, Sep 16 2019

(GAP) a:=[4, 12, 36, 108, 324, 972, 2916, 8748, 26244, 78726];; for n in [11..30] do a[n]:=2*Sum([1..9], j-> a[n-j]) -3*a[n-10]; od; Concatenation([1], a); # G. C. Greubel, Sep 16 2019

CROSSREFS

Sequence in context: A164353 A164697 A165184 * A166328 A166468 A166858

Adjacent sequences:  A165753 A165754 A165755 * A165757 A165758 A165759

KEYWORD

nonn

AUTHOR

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

STATUS

approved

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Last modified April 20 19:27 EDT 2021. Contains 343137 sequences. (Running on oeis4.)