A169423 Number of reduced words of length n in Coxeter group on 26 generators S_i with relations (S_i)^2 = (S_i S_j)^32 = I.

1, 26, 650, 16250, 406250, 10156250, 253906250, 6347656250, 158691406250, 3967285156250, 99182128906250, 2479553222656250, 61988830566406250, 1549720764160156250, 38743019104003906250, 968575477600097656250

Offset

0,2

Comments

The initial terms coincide with those of A170745, although the two sequences are eventually different.

First disagreement is at index 32, the difference is 325. - Klaus Brockhaus, Jun 27 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 (24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, -300).

Formula

G.f.: (t^32 + 2*t^31 + 2*t^30 + 2*t^29 + 2*t^28 + 2*t^27 + 2*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)/(300*t^32 - 24*t^31 - 24*t^30 - 24*t^29 - 24*t^28 - 24*t^27 - 24*t^26 - 24*t^25 - 24*t^24 - 24*t^23 - 24*t^22 - 24*t^21 - 24*t^20 - 24*t^19 - 24*t^18 - 24*t^17 - 24*t^16 - 24*t^15 - 24*t^14 - 24*t^13 - 24*t^12 - 24*t^11 - 24*t^10 - 24*t^9 - 24*t^8 - 24*t^7 - 24*t^6 - 24*t^5 - 24*t^4 - 24*t^3 - 24*t^2 - 24*t + 1).

G.f.: (1+2*sum(k=1..31, x^k)+x^32)/(1-24*sum(k=1..31, x^k)+300*x^32).

Mathematica

coxG[{32, 300, -24}] (* The coxG program is at A169452 *) (* Harvey P. Dale, Jul 31 2019 *)

Crossrefs

Cf. A170745 (G.f.: (1+x)/(1-25*x) ).

Sequence in context: A169279 A169327 A169375 * A169471 A169519 A169567

Adjacent sequences: A169420 A169421 A169422 * A169424 A169425 A169426

Keyword

nonn

Author

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

Status

approved