A170001 Number of reduced words of length n in Coxeter group on 40 generators S_i with relations (S_i)^2 = (S_i S_j)^35 = 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, -741).

Formula

G.f. (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^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)

Crossrefs

Sequence in context: A169437 A169485 A169533 * A170049 A170097 A170145

Adjacent sequences: A169998 A169999 A170000 * A170002 A170003 A170004

Keyword

nonn

Author

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

Status

approved