A169283 Number of reduced words of length n in Coxeter group on 30 generators S_i with relations (S_i)^2 = (S_i S_j)^29 = 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 29: a(29) = 2656227054994356346098442980756223579120395, A170749(29) = 2656227054994356346098442980756223579120830. - Klaus Brockhaus, Jun 03 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, 28, 28, 28, 28, 28, 28, -406).

Formula

G.f.: (t^29 + 2*t^28 + 2*t^27 + 2*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)/(406*t^29 - 28*t^28 - 28*t^27 - 28*t^26 - 28*t^25 - 28*t^24 - 28*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[28]]+1+t^29, den=Total[-28 t^Range[28]]+ 1+ 406t^29}, CoefficientList[Series[num/den, {t, 0, 20}], t]] (* Harvey P. Dale, Jun 15 2011 *)

Crossrefs

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

Sequence in context: A169139 A169187 A169235 * A169331 A169379 A169427

Adjacent sequences: A169280 A169281 A169282 * A169284 A169285 A169286

Keyword

nonn

Author

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

Status

approved