A170577 Number of reduced words of length n in Coxeter group on 40 generators S_i with relations (S_i)^2 = (S_i S_j)^47 = I.

1, 40, 1560, 60840, 2372760, 92537640, 3608967960, 140749750440, 5489240267160, 214080370419240, 8349134446350360, 325616243407664040, 12699033492898897560, 495262306223057004840, 19315229942699223188760

Offset

0,2

Comments

The initial terms coincide with those of A170759, 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..14.

Index entries for linear recurrences with constant coefficients, signature (38, 38, 38, 38, 38, 38, 38, 38, 38, 38, 38, 38, 38, 38, 38, 38, 38, 38, 38, 38, 38, 38, 38, 38, 38, 38, 38, 38, 38, 38, 38, 38, 38, 38, 38, 38, 38, 38, 38, 38, 38, 38, 38, 38, 38, 38, -741).

Formula

G.f. (t^47 + 2*t^46 + 2*t^45 + 2*t^44 + 2*t^43 + 2*t^42 + 2*t^41 + 2*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)/(741*t^47 -

38*t^46 - 38*t^45 - 38*t^44 - 38*t^43 - 38*t^42 - 38*t^41 - 38*t^40 -

38*t^39 - 38*t^38 - 38*t^37 - 38*t^36 - 38*t^35 - 38*t^34 - 38*t^33 -

38*t^32 - 38*t^31 - 38*t^30 - 38*t^29 - 38*t^28 - 38*t^27 - 38*t^26 -

38*t^25 - 38*t^24 - 38*t^23 - 38*t^22 - 38*t^21 - 38*t^20 - 38*t^19 -

38*t^18 - 38*t^17 - 38*t^16 - 38*t^15 - 38*t^14 - 38*t^13 - 38*t^12 -

38*t^11 - 38*t^10 - 38*t^9 - 38*t^8 - 38*t^7 - 38*t^6 - 38*t^5 - 38*t^4

- 38*t^3 - 38*t^2 - 38*t + 1)

Mathematica

With[{num=Total[2t^Range[46]]+t^47+1, den=Total[-38 t^Range[46]]+ 741t^47+ 1}, CoefficientList[Series[num/den, {t, 0, 30}], t]] (* Harvey P. Dale, Jan 21 2013 *)

Crossrefs

Sequence in context: A170433 A170481 A170529 * A170625 A170673 A170721

Adjacent sequences: A170574 A170575 A170576 * A170578 A170579 A170580

Keyword

nonn

Author

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

Status

approved