A168851 Number of reduced words of length n in Coxeter group on 30 generators S_i with relations (S_i)^2 = (S_i S_j)^20 = 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 20: a(20) = 183097837397699744687365489635, A170749(20) = 183097837397699744687365490070. - Klaus Brockhaus, Apr 02 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, -406).

Formula

G.f.: (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^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

coxG[{20, 406, -28}] (* The coxG program is at A169452 *) (* Harvey P. Dale, Jun 04 2016 *)

Crossrefs

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

Sequence in context: A168707 A168755 A168803 * A168899 A168947 A168995

Adjacent sequences: A168848 A168849 A168850 * A168852 A168853 A168854

Keyword

nonn

Author

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

Status

approved