A169230 Number of reduced words of length n in Coxeter group on 25 generators S_i with relations (S_i)^2 = (S_i S_j)^28 = 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 at index 28: a(28) = 460939084479458193409602557014808985300, A170744(28) = 460939084479458193409602557014808985600. - Klaus Brockhaus, May 24 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, -276).

Formula

G.f.: (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^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).

Mathematica

With[{num=Total[2t^Range[27]]+t^28+1, den=Total[-23 t^Range[27]]+ 276t^28+ 1}, CoefficientList[Series[num/den, {t, 0, 20}], t]] (* Harvey P. Dale, Nov 04 2011 *)

Crossrefs

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

Sequence in context: A169086 A169134 A169182 * A169278 A169326 A169374

Adjacent sequences: A169227 A169228 A169229 * A169231 A169232 A169233

Keyword

nonn

Author

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

Status

approved