A165368 Number of reduced words of length n in Coxeter group on 25 generators S_i with relations (S_i)^2 = (S_i S_j)^9 = I.

1, 25, 600, 14400, 345600, 8294400, 199065600, 4777574400, 114661785600, 2751882854100, 66045188491200, 1585084523616300, 38042028562651200, 913008685404268800, 21912208447317811200, 525893002678396108800

Offset

0,2

Comments

The initial terms coincide with those of A170744, although the two sequences are eventually different.

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 (23, 23, 23, 23, 23, 23, 23, 23, -276).

Formula

G.f. (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)/(276*t^9 - 23*t^8 - 23*t^7 - 23*t^6 - 23*t^5 - 23*t^4 - 23*t^3 -

23*t^2 - 23*t + 1)

Mathematica

coxG[{9, 276, -23}] (* The coxG program is at A169452 *) (* Harvey P. Dale, Sep 07 2023 *)

Crossrefs

Sequence in context: A163993 A164638 A164963 * A165967 A166419 A166612

Adjacent sequences: A165365 A165366 A165367 * A165369 A165370 A165371

Keyword

nonn

Author

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

Status

approved