A168914 - OEIS

A168914

Number of reduced words of length n in Coxeter group on 45 generators S_i with relations (S_i)^2 = (S_i S_j)^21 = I.

1, 45, 1980, 87120, 3833280, 168664320, 7421230080, 326534123520, 14367501434880, 632170063134720, 27815482777927680, 1223881242228817920, 53850774658067988480, 2369434084954991493120, 104255099738019625697280

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OFFSET

0,2

COMMENTS

The initial terms coincide with those of A170764, although the two sequences are eventually different.

First disagreement at index 21: a(21) = 33286339890656766317672687122512930, A170764(21) = 33286339890656766317672687122513920. - Klaus Brockhaus, Apr 08 2011

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

LINKS

Table of n, a(n) for n=0..14.

Index entries for linear recurrences with constant coefficients, signature (43, 43, 43, 43, 43, 43, 43, 43, 43, 43, 43, 43, 43, 43, 43, 43, 43, 43, 43, 43, -946).

FORMULA

G.f.: (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)/(946*t^21 - 43*t^20 - 43*t^19 - 43*t^18 - 43*t^17 - 43*t^16 - 43*t^15 - 43*t^14 - 43*t^13 - 43*t^12 - 43*t^11 - 43*t^10 - 43*t^9 - 43*t^8 - 43*t^7 - 43*t^6 - 43*t^5 - 43*t^4 - 43*t^3 - 43*t^2 - 43*t + 1).

MATHEMATICA

coxG[{21, 946, -43}] (* The coxG program is at A169452 *) (* Harvey P. Dale, Jan 23 2019 *)

CROSSREFS

Cf. A170764 (G.f.: (1+x)/(1-44*x)).

Sequence in context: A168770 A168818 A168866 * A168962 A169010 A169058

Adjacent sequences: A168911 A168912 A168913 * A168915 A168916 A168917

KEYWORD

nonn

AUTHOR

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

STATUS

approved