A169137 Number of reduced words of length n in Coxeter group on 28 generators S_i with relations (S_i)^2 = (S_i S_j)^26 = I.

1, 28, 756, 20412, 551124, 14880348, 401769396, 10847773692, 292889889684, 7908027021468, 213516729579636, 5764951698650172, 155653695863554644, 4202649788315975388, 113471544284531335476, 3063731695682346057852

Offset

0,2

Comments

The initial terms coincide with those of A170747, although the two sequences are eventually different.

First disagreement at index 26: a(26) = 17031470055974015855351151793328116218, A170747(26) = 17031470055974015855351151793328116596. - Klaus Brockhaus, Apr 30 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 (26, 26, 26, 26, 26, 26, 26, 26, 26, 26, 26, 26, 26, 26, 26, 26, 26, 26, 26, 26, 26, 26, 26, 26, 26, -351).

Formula

G.f.: (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)/(351*t^26 - 26*t^25 - 26*t^24 - 26*t^23 - 26*t^22 - 26*t^21 - 26*t^20 - 26*t^19 - 26*t^18 - 26*t^17 - 26*t^16 - 26*t^15 - 26*t^14 - 26*t^13 - 26*t^12 - 26*t^11 - 26*t^10 - 26*t^9 - 26*t^8 - 26*t^7 - 26*t^6 - 26*t^5 - 26*t^4 - 26*t^3 - 26*t^2 - 26*t + 1).

Mathematica

coxG[{26, 351, -26}] (* The coxG program is at A169452 *) (* Harvey P. Dale, May 05 2021 *)

Crossrefs

Cf. A170747 (G.f.: (1+x)/(1-27*x)).

Sequence in context: A168993 A169041 A169089 * A169185 A169233 A169281

Adjacent sequences: A169134 A169135 A169136 * A169138 A169139 A169140

Keyword

nonn

Author

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

Status

approved