A170664 Number of reduced words of length n in Coxeter group on 31 generators S_i with relations (S_i)^2 = (S_i S_j)^49 = 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, 29, 29, 29, 29, 29, 29, -435).

Formula

G.f. (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)/(435*t^49 - 29*t^48 - 29*t^47 - 29*t^46 - 29*t^45 - 29*t^44 - 29*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[48]]+t^49+1, den=Total[-29 t^Range[48]]+435t^49+ 1}, CoefficientList[Series[num/den, {t, 0, 20}], t]] (* Harvey P. Dale, Apr 01 2013 *)

Crossrefs

Sequence in context: A170520 A170568 A170616 * A170712 A170750 A218733

Adjacent sequences: A170661 A170662 A170663 * A170665 A170666 A170667

Keyword

nonn

Author

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

Status

approved