A170500 Number of reduced words of length n in Coxeter group on 11 generators S_i with relations (S_i)^2 = (S_i S_j)^46 = I.

1, 11, 110, 1100, 11000, 110000, 1100000, 11000000, 110000000, 1100000000, 11000000000, 110000000000, 1100000000000, 11000000000000, 110000000000000, 1100000000000000, 11000000000000000, 110000000000000000

Offset

0,2

Comments

The initial terms coincide with those of A003953, 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..17.

Index entries for linear recurrences with constant coefficients, signature (9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, -45).

Formula

G.f. (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)/(45*t^46 - 9*t^45 -

9*t^44 - 9*t^43 - 9*t^42 - 9*t^41 - 9*t^40 - 9*t^39 - 9*t^38 - 9*t^37 -

9*t^36 - 9*t^35 - 9*t^34 - 9*t^33 - 9*t^32 - 9*t^31 - 9*t^30 - 9*t^29 -

9*t^28 - 9*t^27 - 9*t^26 - 9*t^25 - 9*t^24 - 9*t^23 - 9*t^22 - 9*t^21 -

9*t^20 - 9*t^19 - 9*t^18 - 9*t^17 - 9*t^16 - 9*t^15 - 9*t^14 - 9*t^13 -

9*t^12 - 9*t^11 - 9*t^10 - 9*t^9 - 9*t^8 - 9*t^7 - 9*t^6 - 9*t^5 - 9*t^4

- 9*t^3 - 9*t^2 - 9*t + 1)

Mathematica

With[{num=Total[2t^Range[45]]+t^46+1, den=Total[-9 t^Range[45]]+45t^46+ 1}, CoefficientList[Series[num/den, {t, 0, 30}], t]] (* Harvey P. Dale, May 11 2014 *)

Crossrefs

Sequence in context: A170356 A170404 A170452 * A170548 A170596 A170644

Adjacent sequences: A170497 A170498 A170499 * A170501 A170502 A170503

Keyword

nonn

Author

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

Status

approved