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A163222 Number of reduced words of length n in Coxeter group on 39 generators S_i with relations (S_i)^2 = (S_i S_j)^4 = I. 1
1, 39, 1482, 56316, 2139267, 81263988, 3086962281, 117263934684, 4454486050560, 169211838474861, 6427822638540342, 244172655087350379, 9275347010187982854, 352341101130365494992, 13384324210123816783899 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

The initial terms coincide with those of A170758, 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..630

Index entries for linear recurrences with constant coefficients, signature (37, 37, 37, -703).

FORMULA

G.f.: (t^4 + 2*t^3 + 2*t^2 + 2*t + 1)/(703*t^4 - 37*t^3 - 37*t^2 - 37*t + 1).

MATHEMATICA

CoefficientList[Series[(t^4+2*t^3+2*t^2+2*t+1)/(703*t^4-37*t^3-37*t^2 - 37*t+1), {t, 0, 20}], t] (* or *) Join[{1}, LinearRecurrence[{37, 37, 37, -703}, {39, 1482, 56316, 2139267}, 20]] (* G. C. Greubel, Dec 11 2016 *)

coxG[{4, 703, -37}] (* The coxG program is at A169452 *) (* G. C. Greubel, Apr 30 2019 *)

PROG

(PARI) my(t='t+O('t^20)); Vec((t^4+2*t^3+2*t^2+2*t+1)/(703*t^4-37*t^3 - 37*t^2-37*t+1)) \\ _G. c. Greubel_, Dec 11 2016

(MAGMA) R<x>:=PowerSeriesRing(Integers(), 20); Coefficients(R!( (1+x)*(1-x^4)/(1-38*x+740*x^4-703*x^5) )); // G. C. Greubel, Apr 30 2019

(Sage) ((1+x)*(1-x^4)/(1-38*x+740*x^4-703*x^5)).series(x, 20).coefficients(x, sparse=False) # G. C. Greubel, Apr 30 2019

CROSSREFS

Sequence in context: A235973 A097314 A162871 * A163668 A164084 A164681

Adjacent sequences:  A163219 A163220 A163221 * A163223 A163224 A163225

KEYWORD

nonn

AUTHOR

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

STATUS

approved

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Last modified November 14 17:24 EST 2019. Contains 329126 sequences. (Running on oeis4.)