A169010 Number of reduced words of length n in Coxeter group on 45 generators S_i with relations (S_i)^2 = (S_i S_j)^23 = I.

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

Offset

0,2

Comments

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

First disagreement at index 23: a(23) = 64442354028311499591014322269186948130, A170764(23) = 64442354028311499591014322269186949120. - Klaus Brockhaus, Apr 19 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, 43, 43, -946).

Formula

G.f.: (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)/(946*t^23 - 43*t^22 - 43*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[{23, 946, -43}] (* The coxG program is at A169452 *) (* Harvey P. Dale, Aug 24 2019 *)

Crossrefs

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

Sequence in context: A168866 A168914 A168962 * A169058 A169106 A169154

Adjacent sequences: A169007 A169008 A169009 * A169011 A169012 A169013

Keyword

nonn

Author

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

Status

approved