A169486 - OEIS

A169486

Number of reduced words of length n in Coxeter group on 41 generators S_i with relations (S_i)^2 = (S_i S_j)^33 = I.

1, 41, 1640, 65600, 2624000, 104960000, 4198400000, 167936000000, 6717440000000, 268697600000000, 10747904000000000, 429916160000000000, 17196646400000000000, 687865856000000000000, 27514634240000000000000

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OFFSET

0,2

COMMENTS

The initial terms coincide with those of A170760, 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 (39, 39, 39, 39, 39, 39, 39, 39, 39, 39, 39, 39, 39, 39, 39, 39, 39, 39, 39, 39, 39, 39, 39, 39, 39, 39, 39, 39, 39, 39, 39, 39, -780).

FORMULA

G.f. (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)/(780*t^33 - 39*t^32 - 39*t^31 - 39*t^30 - 39*t^29 - 39*t^28 - 39*t^27

- 39*t^26 - 39*t^25 - 39*t^24 - 39*t^23 - 39*t^22 - 39*t^21 - 39*t^20 -

39*t^19 - 39*t^18 - 39*t^17 - 39*t^16 - 39*t^15 - 39*t^14 - 39*t^13 -

39*t^12 - 39*t^11 - 39*t^10 - 39*t^9 - 39*t^8 - 39*t^7 - 39*t^6 - 39*t^5

- 39*t^4 - 39*t^3 - 39*t^2 - 39*t + 1)

MATHEMATICA

coxG[{33, 780, -39}] (* The coxG program is at A169452 *) (* Harvey P. Dale, Sep 27 2014 *)

CROSSREFS

Sequence in context: A169342 A169390 A169438 * A169534 A170002 A170050

Adjacent sequences: A169483 A169484 A169485 * A169487 A169488 A169489

KEYWORD

nonn

AUTHOR

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

STATUS

approved