A169161 - OEIS

A169161

Number of reduced words of length n in Coxeter group on 4 generators S_i with relations (S_i)^2 = (S_i S_j)^27 = I.

1, 4, 12, 36, 108, 324, 972, 2916, 8748, 26244, 78732, 236196, 708588, 2125764, 6377292, 19131876, 57395628, 172186884, 516560652, 1549681956, 4649045868, 13947137604, 41841412812, 125524238436, 376572715308, 1129718145924

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OFFSET

0,2

COMMENTS

The initial terms coincide with those of A003946, although the two sequences are eventually different.

First disagreement at index 27: a(27) = 10167463313310, A003946(27) = 10167463313316. - Klaus Brockhaus, May 07 2011

Computed with MAGMA using commands similar to those used to compute A154638.

LINKS

Table of n, a(n) for n=0..25.

Index entries for linear recurrences with constant coefficients, signature (2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, -3).

FORMULA

G.f.: (t^27 + 2*t^26 + 2*t^25 + 2*t^24 + 2*t^23 + 2*t^22 + 2*t^21 + 2*t^20 + 2*t^19 + 2*t^18 + 2*t^17 + 2*t^16 + 2*t^15 + 2*t^14 + 2*t^13 + 2*t^12 + 2*t^11 + 2*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^27 - 2*t^26 - 2*t^25 - 2*t^24 - 2*t^23 - 2*t^22 - 2*t^21 - 2*t^20 - 2*t^19 - 2*t^18 - 2*t^17 - 2*t^16 - 2*t^15 - 2*t^14 - 2*t^13 - 2*t^12 - 2*t^11 - 2*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).

MATHEMATICA

coxG[{27, 3, -2, 30}] (* The coxG program is at A169452 *) (* Harvey P. Dale, Sep 26 2020 *)

CROSSREFS

Cf. A003946 (G.f.: (1+x)/(1-3*x)).

Sequence in context: A003946 A052156 A169113 * A169209 A169257 A169305

Adjacent sequences: A169158 A169159 A169160 * A169162 A169163 A169164

KEYWORD

nonn

AUTHOR

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

STATUS

approved