A169003 Number of reduced words of length n in Coxeter group on 38 generators S_i with relations (S_i)^2 = (S_i S_j)^23 = 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 23: a(23) = 1202877845307046799279672294496960919, A170757(23) = 1202877845307046799279672294496961622. - Klaus Brockhaus, Apr 19 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 (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^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^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[22]]+t^23+1, den=Total[-36 t^Range[22]]+ 666t^23+1}, CoefficientList[Series[num/den, {t, 0, 20}], t]] (* Harvey P. Dale, Jul 24 2011 *)

Crossrefs

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

Sequence in context: A168859 A168907 A168955 * A169051 A169099 A169147

Adjacent sequences: A169000 A169001 A169002 * A169004 A169005 A169006

Keyword

nonn

Author

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

Status

approved