A169045 Number of reduced words of length n in Coxeter group on 32 generators S_i with relations (S_i)^2 = (S_i S_j)^24 = I.

1, 32, 992, 30752, 953312, 29552672, 916132832, 28400117792, 880403651552, 27292513198112, 846067909141472, 26228105183385632, 813071260684954592, 25205209081233592352, 781361481518241362912, 24222205927065482250272

Offset

0,2

Comments

The initial terms coincide with those of A170751, although the two sequences are eventually different.

First disagreement at index 24: a(24) = 640425972609576968452439175817452016, A170751(24) = 640425972609576968452439175817452512. - Klaus Brockhaus, Apr 20 2011

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

Links

Table of n, a(n) for n=0..15.

Index entries for linear recurrences with constant coefficients, signature (30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, -465).

Formula

G.f.: (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)/(465*t^24 - 30*t^23 - 30*t^22 - 30*t^21 - 30*t^20 - 30*t^19 - 30*t^18 - 30*t^17 - 30*t^16 - 30*t^15 - 30*t^14 - 30*t^13 - 30*t^12 - 30*t^11 - 30*t^10 - 30*t^9 - 30*t^8 - 30*t^7 - 30*t^6 - 30*t^5 - 30*t^4 - 30*t^3 - 30*t^2 - 30*t + 1).

Mathematica

coxG[{24, 465, -30}] (* The coxG program is at A169452 *) (* Harvey P. Dale, Feb 05 2019 *)

Crossrefs

Cf. A170751 (G.f.: (1+x)/(1-31*x)).

Sequence in context: A168901 A168949 A168997 * A169093 A169141 A169189

Adjacent sequences: A169042 A169043 A169044 * A169046 A169047 A169048

Keyword

nonn

Author

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

Status

approved