A170033 Number of reduced words of length n in Coxeter group on 24 generators S_i with relations (S_i)^2 = (S_i S_j)^36 = 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.

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 (22, 22, 22, 22, 22, 22, 22, 22, 22, 22, 22, 22, 22, 22, 22, 22, 22, 22, 22, 22, 22, 22, 22, 22, 22, 22, 22, 22, 22, 22, 22, 22, 22, 22, 22, -253).

Formula

G.f. (t^36 + 2*t^35 + 2*t^34 + 2*t^33 + 2*t^32 + 2*t^31 + 2*t^30 + 2*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)/(253*t^36 - 22*t^35 - 22*t^34 - 22*t^33 -

22*t^32 - 22*t^31 - 22*t^30 - 22*t^29 - 22*t^28 - 22*t^27 - 22*t^26 -

22*t^25 - 22*t^24 - 22*t^23 - 22*t^22 - 22*t^21 - 22*t^20 - 22*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

With[{num=Total[2t^Range[35]]+t^36+1, den=Total[-22 t^Range[35]]+ 253t^36+ 1}, CoefficientList[Series[num/den, {t, 0, 20}], t]] (* Harvey P. Dale, Nov 16 2011 *)

Crossrefs

Sequence in context: A169469 A169517 A169565 * A170081 A170129 A170177

Adjacent sequences: A170030 A170031 A170032 * A170034 A170035 A170036

Keyword

nonn

Author

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

Status

approved