A169104 Number of reduced words of length n in Coxeter group on 43 generators S_i with relations (S_i)^2 = (S_i S_j)^25 = I.

1, 43, 1806, 75852, 3185784, 133802928, 5619722976, 236028364992, 9913191329664, 416354035845888, 17486869505527296, 734448519232146432, 30846837807750150144, 1295567187925506306048, 54413821892871264854016

Offset

0,2

Comments

The initial terms coincide with those of A170762, although the two sequences are eventually different.

First disagreement at index 25: a(25) = 39034752056493120297937181778758470728825, A170762(25) = 39034752056493120297937181778758470729728. - Klaus Brockhaus, Apr 25 2011

Computed with MAGMA using commands similar to those used to compute A154638.

Links

Table of n, a(n) for n=0..14.

Index entries for linear recurrences with constant coefficients, signature (41, 41, 41, 41, 41, 41, 41, 41, 41, 41, 41, 41, 41, 41, 41, 41, 41, 41, 41, 41, 41, 41, 41, 41, -861).

Formula

G.f.: (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)/(861*t^25 - 41*t^24 - 41*t^23 - 41*t^22 - 41*t^21 - 41*t^20 - 41*t^19 - 41*t^18 - 41*t^17 - 41*t^16 - 41*t^15 - 41*t^14 - 41*t^13 - 41*t^12 - 41*t^11 - 41*t^10 - 41*t^9 - 41*t^8 - 41*t^7 - 41*t^6 - 41*t^5 - 41*t^4 - 41*t^3 - 41*t^2 - 41*t + 1).

Mathematica

With[{num=Total[2t^Range[24]]+t^25+1, den=Total[-41 t^Range[24]]+ 861t^25+ 1}, CoefficientList[Series[num/den, {t, 0, 20}], t]] (* Harvey P. Dale, Nov 29 2011 *)

Crossrefs

Cf. A170762 (G.f.: (1+x)/(1-42*x)).

Sequence in context: A168960 A169008 A169056 * A169152 A169200 A169248

Adjacent sequences: A169101 A169102 A169103 * A169105 A169106 A169107

Keyword

nonn

Author

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

Status

approved