A170236 Number of reduced words of length n in Coxeter group on 35 generators S_i with relations (S_i)^2 = (S_i S_j)^40 = I.

1, 35, 1190, 40460, 1375640, 46771760, 1590239840, 54068154560, 1838317255040, 62502786671360, 2125094746826240, 72253221392092160, 2456609527331133440, 83524723929258536960, 2839840613594790256640, 96554580862222868725760

Offset

0,2

Comments

The initial terms coincide with those of A170754, 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 (33, 33, 33, 33, 33, 33, 33, 33, 33, 33, 33, 33, 33, 33, 33, 33, 33, 33, 33, 33, 33, 33, 33, 33, 33, 33, 33, 33, 33, 33, 33, 33, 33, 33, 33, 33, 33, 33, 33, -561).

Formula

G.f. (t^40 + 2*t^39 + 2*t^38 + 2*t^37 + 2*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)/(561*t^40 - 33*t^39 - 33*t^38 - 33*t^37 - 33*t^36 - 33*t^35 - 33*t^34

- 33*t^33 - 33*t^32 - 33*t^31 - 33*t^30 - 33*t^29 - 33*t^28 - 33*t^27 -

33*t^26 - 33*t^25 - 33*t^24 - 33*t^23 - 33*t^22 - 33*t^21 - 33*t^20 -

33*t^19 - 33*t^18 - 33*t^17 - 33*t^16 - 33*t^15 - 33*t^14 - 33*t^13 -

33*t^12 - 33*t^11 - 33*t^10 - 33*t^9 - 33*t^8 - 33*t^7 - 33*t^6 - 33*t^5

- 33*t^4 - 33*t^3 - 33*t^2 - 33*t + 1)

Mathematica

With[{num=Total[2t^Range[39]]+t^40+1, den=Total[-33 t^Range[39]]+ 561t^40+1}, CoefficientList[Series[num/den, {t, 0, 20}], t]] (* Harvey P. Dale, Apr 09 2012 *)

Crossrefs

Sequence in context: A170092 A170140 A170188 * A170284 A170332 A170380

Adjacent sequences: A170233 A170234 A170235 * A170237 A170238 A170239

Keyword

nonn

Author

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

Status

approved