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A170708 Number of reduced words of length n in Coxeter group on 27 generators S_i with relations (S_i)^2 = (S_i S_j)^50 = I. 1
1, 27, 702, 18252, 474552, 12338352, 320797152, 8340725952, 216858874752, 5638330743552, 146596599332352, 3811511582641152, 99099301148669952, 2576581829865418752, 66991127576500887552, 1741769316989023076352 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

The initial terms coincide with those of A170746, although the two sequences are eventually different.

Computed with MAGMA using commands similar to those used to compute A154638.

About the initial comment, first disagreement is at index 50 and the difference is 351.  - Vincenzo Librandi, Dec 06 2012]

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 0..200

Index entries for linear recurrences with constant coefficients, signature (25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, 25, -325).

FORMULA

G.f. (t^50 + 2*t^49 + 2*t^48 + 2*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)/(325*t^50 - 25*t^49 - 25*t^48 - 25*t^47 - 25*t^46 - 25*t^45 - ,25*t^44 - 25*t^43 - 25*t^42 - 25*t^41 - 25*t^40 - 25*t^39 - 25*t^38 - ,25*t^37 - 25*t^36 - 25*t^35 - 25*t^34 - 25*t^33 - 25*t^32 - 25*t^31 - ,25*t^30 - 25*t^29 - 25*t^28 - 25*t^27 - 25*t^26 - 25*t^25 - 25*t^24 - ,25*t^23 - 25*t^22 - 25*t^21 - 25*t^20 - 25*t^19 - 25*t^18 - 25*t^17 - ,25*t^16 - 25*t^15 - 25*t^14 - 25*t^13 - 25*t^12 - 25*t^11 - 25*t^10 - ,25*t^9 - 25*t^8 - 25*t^7 - 25*t^6 - 25*t^5 - 25*t^4 - 25*t^3 - 25*t^2 - ,25*t + 1).

MATHEMATICA

With[{num = Total[2 t^Range[49]] + t^50 + 1, den = Total[-25 t^Range[49]] + 325 t^50 + 1}, CoefficientList[Series[num/den, {t, 0, 30}], t]] (* Vincenzo Librandi, Dec 06 2012 *)

coxG[{50, 325, -25}] (* The coxG program is at A169452 *) (* Harvey P. Dale, May 07 2019 *)

CROSSREFS

Sequence in context: A170564 A170612 A170660 * A170746 A218729 A171332

Adjacent sequences:  A170705 A170706 A170707 * A170709 A170710 A170711

KEYWORD

nonn

AUTHOR

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

STATUS

approved

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Last modified May 28 09:09 EDT 2022. Contains 354112 sequences. (Running on oeis4.)