A169147 Number of reduced words of length n in Coxeter group on 38 generators S_i with relations (S_i)^2 = (S_i S_j)^26 = I.

1, 38, 1406, 52022, 1924814, 71218118, 2635070366, 97497603542, 3607411331054, 133474219248998, 4938546112212926, 182726206151878262, 6760869627619495694, 250152176221921340678, 9255630520211089605086

Offset

0,2

Comments

The initial terms coincide with those of A170757, although the two sequences are eventually different.

First disagreement at index 26: a(26) = 60929371498337841523913240733154597038463, A170757(26) = 60929371498337841523913240733154597039166. - Klaus Brockhaus, Apr 30 2011

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

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..200

Index entries for linear recurrences with constant coefficients, signature (36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, -666).

Formula

G.f.: (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)/(666*t^26 - 36*t^25 - 36*t^24 - 36*t^23 - 36*t^22 - 36*t^21 - 36*t^20 - 36*t^19 - 36*t^18 - 36*t^17 - 36*t^16 - 36*t^15 - 36*t^14 - 36*t^13 - 36*t^12 - 36*t^11 - 36*t^10 - 36*t^9 - 36*t^8 - 36*t^7 - 36*t^6 - 36*t^5 - 36*t^4 - 36*t^3 - 36*t^2 - 36*t + 1).

Mathematica

With[{num=Total[2t^Range[25]]+t^26+1, den=Total[-36 t^Range[25]]+666t^26+ 1}, CoefficientList[Series[num/den, {t, 0, 20}], t]] (* Harvey P. Dale, Apr 23 2014 *)

Crossrefs

Cf. A170757 (G.f.: (1+x)/(1-37*x)).

Sequence in context: A169003 A169051 A169099 * A169195 A169243 A169291

Adjacent sequences: A169144 A169145 A169146 * A169148 A169149 A169150

Keyword

nonn

Author

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

Status

approved