A168797 Number of reduced words of length n in Coxeter group on 24 generators S_i with relations (S_i)^2 = (S_i S_j)^19 = I.

1, 24, 552, 12696, 292008, 6716184, 154472232, 3552861336, 81715810728, 1879463646744, 43227663875112, 994236269127576, 22867434189934248, 525950986368487704, 12096872686475217192, 278228071788929995416

Offset

0,2

Comments

The initial terms coincide with those of A170743, although the two sequences are eventually different.

First disagreement at index 19: a(19) = 77859621837485958847208580, A170743(19) = 77859621837485958847208856. - Klaus Brockhaus, Apr 01 2011

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

Links

G. C. Greubel, Table of n, a(n) for n = 0..500

Index entries for linear recurrences with constant coefficients, signature (22, 22, 22, 22, 22, 22, 22, 22, 22, 22, 22, 22, 22, 22, 22, 22, 22, 22, -253).

Formula

G.f.: (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)/(253*t^19 - 22*t^18 - 22*t^17 - 22*t^16 - 22*t^15 - 22*t^14 - 22*t^13 - 22*t^12 - 22*t^11 - 22*t^10 - 22*t^9 - 22*t^8 - 22*t^7 - 22*t^6 - 22*t^5 - 22*t^4 - 22*t^3 - 22*t^2 - 22*t + 1).

Mathematica

CoefficientList[Series[(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)/(253*t^19 - 22*t^18 - 22*t^17 - 22*t^16 - 22*t^15 - 22*t^14 - 22*t^13 - 22*t^12 - 22*t^11 - 22*t^10 - 22*t^9 - 22*t^8 - 22*t^7 - 22*t^6 - 22*t^5 - 22*t^4 - 22*t^3 - 22*t^2 - 22*t + 1), {t, 0, 50}], t] (* G. C. Greubel, Aug 16 2016 *)
coxG[{19, 253, -22}] (* The coxG program is at A169452 *) (* Harvey P. Dale, Feb 09 2025 *)

Crossrefs

Cf. A170743 (G.f.: (1+x)/(1-23*x)).

Sequence in context: A167938 A168701 A168749 * A168845 A168893 A168941

Adjacent sequences: A168794 A168795 A168796 * A168798 A168799 A168800

Keyword

nonn

Author

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

Status

approved