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A169437 Number of reduced words of length n in Coxeter group on 40 generators S_i with relations (S_i)^2 = (S_i S_j)^32 = I. 0
1, 40, 1560, 60840, 2372760, 92537640, 3608967960, 140749750440, 5489240267160, 214080370419240, 8349134446350360, 325616243407664040, 12699033492898897560, 495262306223057004840, 19315229942699223188760 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

The initial terms coincide with those of A170759, although the two sequences are eventually different.

First disagreement is at index 32, the difference is 780. - Klaus Brockhaus, Jun 30 2011

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, -741).

FORMULA

G.f.: (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^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).

G.f.: (1+2*sum(k=1..31,x^k)+x^32)/(1-38*sum(k=1..31,x^k)+741*x^32).

MATHEMATICA

coxG[{32, 741, -38}] (* The coxG program is at A169452 *) (* Harvey P. Dale, Feb 11 2015 *)

CROSSREFS

Cf. A170759 (G.f.: (1+x)/(1-39*x) ).

Sequence in context: A169293 A169341 A169389 * A169485 A169533 A170001

Adjacent sequences:  A169434 A169435 A169436 * A169438 A169439 A169440

KEYWORD

nonn

AUTHOR

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

STATUS

approved

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Last modified September 24 11:38 EDT 2020. Contains 337318 sequences. (Running on oeis4.)