A170376 Number of reduced words of length n in Coxeter group on 31 generators S_i with relations (S_i)^2 = (S_i S_j)^43 = I.

1, 31, 930, 27900, 837000, 25110000, 753300000, 22599000000, 677970000000, 20339100000000, 610173000000000, 18305190000000000, 549155700000000000, 16474671000000000000, 494240130000000000000, 14827203900000000000000

Offset

0,2

Comments

The initial terms coincide with those of A170750, 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 (29, 29, 29, 29, 29, 29, 29, 29, 29, 29, 29, 29, 29, 29, 29, 29, 29, 29, 29, 29, 29, 29, 29, 29, 29, 29, 29, 29, 29, 29, 29, 29, 29, 29, 29, 29, 29, 29, 29, 29, 29, 29, -435).

Formula

G.f. (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)/(435*t^43 - 29*t^42 - 29*t^41 - 29*t^40 - 29*t^39 -

29*t^38 - 29*t^37 - 29*t^36 - 29*t^35 - 29*t^34 - 29*t^33 - 29*t^32 -

29*t^31 - 29*t^30 - 29*t^29 - 29*t^28 - 29*t^27 - 29*t^26 - 29*t^25 -

29*t^24 - 29*t^23 - 29*t^22 - 29*t^21 - 29*t^20 - 29*t^19 - 29*t^18 -

29*t^17 - 29*t^16 - 29*t^15 - 29*t^14 - 29*t^13 - 29*t^12 - 29*t^11 -

29*t^10 - 29*t^9 - 29*t^8 - 29*t^7 - 29*t^6 - 29*t^5 - 29*t^4 - 29*t^3 -

29*t^2 - 29*t + 1)

Mathematica

With[{num=Total[2t^Range[42]]+t^43+1, den=Total[-29 t^Range[42]]+435t^43+ 1}, CoefficientList[Series[num/den, {t, 0, 20}], t]] (* Harvey P. Dale, Jun 26 2013 *)
coxG[{43, 435, -29}] (* The coxG program is at A169452 *) (* Harvey P. Dale, Sep 29 2024 *)

Crossrefs

Sequence in context: A170232 A170280 A170328 * A170424 A170472 A170520

Adjacent sequences: A170373 A170374 A170375 * A170377 A170378 A170379

Keyword

nonn

Author

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

Status

approved