A170174 Number of reduced words of length n in Coxeter group on 21 generators S_i with relations (S_i)^2 = (S_i S_j)^39 = I.

1, 21, 420, 8400, 168000, 3360000, 67200000, 1344000000, 26880000000, 537600000000, 10752000000000, 215040000000000, 4300800000000000, 86016000000000000, 1720320000000000000, 34406400000000000000

Offset

0,2

Comments

The initial terms coincide with those of A170740, 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 (19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, -190).

Formula

G.f. (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)/(190*t^39 -

19*t^38 - 19*t^37 - 19*t^36 - 19*t^35 - 19*t^34 - 19*t^33 - 19*t^32 -

19*t^31 - 19*t^30 - 19*t^29 - 19*t^28 - 19*t^27 - 19*t^26 - 19*t^25 -

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

19*t^17 - 19*t^16 - 19*t^15 - 19*t^14 - 19*t^13 - 19*t^12 - 19*t^11 -

19*t^10 - 19*t^9 - 19*t^8 - 19*t^7 - 19*t^6 - 19*t^5 - 19*t^4 - 19*t^3 -

19*t^2 - 19*t + 1)

Mathematica

With[{num=Total[2t^Range[38]]+t^39+1, den=Total[-19 t^Range[38]]+190t^39+ 1}, CoefficientList[Series[num/den, {t, 0, 20}], t]] (* Harvey P. Dale, May 19 2014 *)

Crossrefs

Sequence in context: A170030 A170078 A170126 * A170222 A170270 A170318

Adjacent sequences: A170171 A170172 A170173 * A170175 A170176 A170177

Keyword

nonn

Author

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

Status

approved