A170429 - OEIS

A170429

Number of reduced words of length n in Coxeter group on 36 generators S_i with relations (S_i)^2 = (S_i S_j)^44 = I.

1, 36, 1260, 44100, 1543500, 54022500, 1890787500, 66177562500, 2316214687500, 81067514062500, 2837362992187500, 99307704726562500, 3475769665429687500, 121651938290039062500, 4257817840151367187500, 149023624405297851562500

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OFFSET

0,2

COMMENTS

The initial terms coincide with those of A170755, 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 (34, 34, 34, 34, 34, 34, 34, 34, 34, 34, 34, 34, 34, 34, 34, 34, 34, 34, 34, 34, 34, 34, 34, 34, 34, 34, 34, 34, 34, 34, 34, 34, 34, 34, 34, 34, 34, 34, 34, 34, 34, 34, 34, -595).

FORMULA

G.f. (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)/(595*t^44 - 34*t^43 - 34*t^42 - 34*t^41 -

34*t^40 - 34*t^39 - 34*t^38 - 34*t^37 - 34*t^36 - 34*t^35 - 34*t^34 -

34*t^33 - 34*t^32 - 34*t^31 - 34*t^30 - 34*t^29 - 34*t^28 - 34*t^27 -

34*t^26 - 34*t^25 - 34*t^24 - 34*t^23 - 34*t^22 - 34*t^21 - 34*t^20 -

34*t^19 - 34*t^18 - 34*t^17 - 34*t^16 - 34*t^15 - 34*t^14 - 34*t^13 -

34*t^12 - 34*t^11 - 34*t^10 - 34*t^9 - 34*t^8 - 34*t^7 - 34*t^6 - 34*t^5

- 34*t^4 - 34*t^3 - 34*t^2 - 34*t + 1)

MATHEMATICA

coxG[{44, 595, -34}] (* The coxG program is at A169452 *) (* Harvey P. Dale, Mar 09 2016 *)

CROSSREFS

Sequence in context: A170285 A170333 A170381 * A170477 A170525 A170573

Adjacent sequences: A170426 A170427 A170428 * A170430 A170431 A170432

KEYWORD

nonn

AUTHOR

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

STATUS

approved