A170078 Number of reduced words of length n in Coxeter group on 21 generators S_i with relations (S_i)^2 = (S_i S_j)^37 = 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, -190).

Formula

G.f. (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^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[36]]+t^37+1, den=Total[-19 t^Range[36]]+190t^37+ 1}, CoefficientList[Series[num/den, {t, 0, 20}], t]] (* Harvey P. Dale, Jun 25 2013 *)

Crossrefs

Sequence in context: A169514 A169562 A170030 * A170126 A170174 A170222

Adjacent sequences: A170075 A170076 A170077 * A170079 A170080 A170081

Keyword

nonn

Author

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

Status

approved