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A163287 Number of reduced words of length n in Coxeter group on 49 generators S_i with relations (S_i)^2 = (S_i S_j)^4 = I. 1
1, 49, 2352, 112896, 5417832, 259999488, 12477267096, 598778820864, 28735144795560, 1378987562102976, 66177035471527512, 3175808211876089664, 152405705797427455464, 7313885981134376257152, 350990324575741067673624 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

The initial terms coincide with those of A170768, 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..590

Index entries for linear recurrences with constant coefficients, signature (47, 47, 47, -1128).

FORMULA

G.f.: (t^4 + 2*t^3 + 2*t^2 + 2*t + 1)/(1128*t^4 - 47*t^3 - 47*t^2 - 47*t + 1).

MATHEMATICA

CoefficientList[Series[(t^4+2*t^3+2*t^2+2*t+1)/(1128*t^4-47*t^3-47*t^2 - 47*t+1), {t, 0, 20}], t] (* or *) LinearRecurrence[{47, 47, 47, -1128}, {1, 49, 2352, 112896, 5417832}, 20] (* G. C. Greubel, Dec 17 2016 *)

coxG[{4, 1128, -47}] (* The coxG program is at A169452 *) (* G. C. Greubel, May 01 2019 *)

PROG

(PARI) my(t='t+O('t^20)); Vec((t^4+2*t^3+2*t^2+2*t+1)/(1128*t^4-47*t^3 - 47*t^2-47*t+1)) \\ G. C. Greubel, Dec 17 2016

(MAGMA) R<x>:=PowerSeriesRing(Integers(), 20); Coefficients(R!( (1+x)*(1-x^4)/(1-48*x+1175*x^4-1128*x^5) )); // G. C. Greubel, May 01 2019

(Sage) ((1+x)*(1-x^4)/(1-48*x+1175*x^4-1128*x^5)).series(x, 20).coefficients(x, sparse=False) # G. C. Greubel, May 01 2019

(GAP) a:=[49, 2352, 112896, 5417832];; for n in [5..20] do a[n]:=47*(a[n-1]+a[n-2] +a[n-3] -24*a[n-4]); od; Concatenation([1], a); # G. C. Greubel, May 01 2019

CROSSREFS

Sequence in context: A061615 A049682 A162914 * A163835 A164350 A164694

Adjacent sequences:  A163284 A163285 A163286 * A163288 A163289 A163290

KEYWORD

nonn

AUTHOR

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

STATUS

approved

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Last modified January 25 03:49 EST 2020. Contains 331241 sequences. (Running on oeis4.)