A168995 Number of reduced words of length n in Coxeter group on 30 generators S_i with relations (S_i)^2 = (S_i S_j)^23 = I.

1, 30, 870, 25230, 731670, 21218430, 615334470, 17844699630, 517496289270, 15007392388830, 435214379276070, 12621216999006030, 366015292971174870, 10614443496164071230, 307818861388758065670, 8926746980273983904430

Offset

0,2

Comments

The initial terms coincide with those of A170749, although the two sequences are eventually different.

First disagreement at index 23: a(23) = 4465573156292499073180156937316795, A170749(23) = 4465573156292499073180156937317230. - 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..15.

Index entries for linear recurrences with constant coefficients, signature (28, 28, 28, 28, 28, 28, 28, 28, 28, 28, 28, 28, 28, 28, 28, 28, 28, 28, 28, 28, 28, 28, -406).

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)/(406*t^23 - 28*t^22 - 28*t^21 - 28*t^20 - 28*t^19 - 28*t^18 - 28*t^17 - 28*t^16 - 28*t^15 - 28*t^14 - 28*t^13 - 28*t^12 - 28*t^11 - 28*t^10 - 28*t^9 - 28*t^8 - 28*t^7 - 28*t^6 - 28*t^5 - 28*t^4 - 28*t^3 - 28*t^2 - 28*t + 1).

Mathematica

With[{num=Total[2t^Range[22]]+t^23+1, den=Total[-28 t^Range[22]]+ 406t^23+ 1}, CoefficientList[Series[num/den, {t, 0, 20}], t]] (* Harvey P. Dale, Oct 05 2011 *)

Crossrefs

Cf. A170749 (G.f.: (1+x)/(1-29*x)).

Sequence in context: A168851 A168899 A168947 * A169043 A169091 A169139

Adjacent sequences: A168992 A168993 A168994 * A168996 A168997 A168998

Keyword

nonn

Author

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

Status

approved