A170041 Number of reduced words of length n in Coxeter group on 32 generators S_i with relations (S_i)^2 = (S_i S_j)^36 = I.

1, 32, 992, 30752, 953312, 29552672, 916132832, 28400117792, 880403651552, 27292513198112, 846067909141472, 26228105183385632, 813071260684954592, 25205209081233592352, 781361481518241362912, 24222205927065482250272

Offset

0,2

Comments

The initial terms coincide with those of A170751, 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 (30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, 30, -465).

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)/(465*t^36 - 30*t^35 - 30*t^34 - 30*t^33 -

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

30*t^25 - 30*t^24 - 30*t^23 - 30*t^22 - 30*t^21 - 30*t^20 - 30*t^19 -

30*t^18 - 30*t^17 - 30*t^16 - 30*t^15 - 30*t^14 - 30*t^13 - 30*t^12 -

30*t^11 - 30*t^10 - 30*t^9 - 30*t^8 - 30*t^7 - 30*t^6 - 30*t^5 - 30*t^4

- 30*t^3 - 30*t^2 - 30*t + 1)

Mathematica

With[{num=Total[2t^Range[35]]+t^36+1, den=Total[-30 t^Range[35]]+ 465t^36+ 1}, CoefficientList[Series[num/den, {t, 0, 20}], t]] (* Harvey P. Dale, Oct 19 2012 *)

Crossrefs

Sequence in context: A169477 A169525 A169573 * A170089 A170137 A170185

Adjacent sequences: A170038 A170039 A170040 * A170042 A170043 A170044

Keyword

nonn

Author

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

Status

approved