A169422 Number of reduced words of length n in Coxeter group on 25 generators S_i with relations (S_i)^2 = (S_i S_j)^32 = I.

1, 25, 600, 14400, 345600, 8294400, 199065600, 4777574400, 114661785600, 2751882854400, 66045188505600, 1585084524134400, 38042028579225600, 913008685901414400, 21912208461633945600, 525893003079214694400

Offset

0,2

Comments

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

First disagreement is at index 32, the difference is 300. - 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 (23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, -276).

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)/(276*t^32 - 23*t^31 - 23*t^30 - 23*t^29 - 23*t^28 - 23*t^27 - 23*t^26 - 23*t^25 - 23*t^24 - 23*t^23 - 23*t^22 - 23*t^21 - 23*t^20 - 23*t^19 - 23*t^18 - 23*t^17 - 23*t^16 - 23*t^15 - 23*t^14 - 23*t^13 - 23*t^12 - 23*t^11 - 23*t^10 - 23*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).

G.f.: (1+2*sum(k=1..31, x^k)+x^32)/(1-23*sum(k=1..31, x^k)+276*x^32).

Crossrefs

Cf. A170744 (G.f.: (1+x)/(1-24*x) ).

Sequence in context: A169278 A169326 A169374 * A169470 A169518 A169566

Adjacent sequences: A169419 A169420 A169421 * A169423 A169424 A169425

Keyword

nonn

Author

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

Status

approved