A170213 Number of reduced words of length n in Coxeter group on 12 generators S_i with relations (S_i)^2 = (S_i S_j)^40 = I.

1, 12, 132, 1452, 15972, 175692, 1932612, 21258732, 233846052, 2572306572, 28295372292, 311249095212, 3423740047332, 37661140520652, 414272545727172, 4556998002998892, 50126978032987812, 551396758362865932

Offset

0,2

Comments

The initial terms coincide with those of A003954, 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 (10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, -55).

Formula

G.f. (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)/(55*t^40 - 10*t^39 - 10*t^38 - 10*t^37 - 10*t^36 - 10*t^35 - 10*t^34

- 10*t^33 - 10*t^32 - 10*t^31 - 10*t^30 - 10*t^29 - 10*t^28 - 10*t^27 -

10*t^26 - 10*t^25 - 10*t^24 - 10*t^23 - 10*t^22 - 10*t^21 - 10*t^20 -

10*t^19 - 10*t^18 - 10*t^17 - 10*t^16 - 10*t^15 - 10*t^14 - 10*t^13 -

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

- 10*t^4 - 10*t^3 - 10*t^2 - 10*t + 1)

Mathematica

coxG[{40, 55, -10}] (* The coxG program is at A169452 *) (* Harvey P. Dale, Jul 19 2015 *)

Crossrefs

Sequence in context: A170069 A170117 A170165 * A170261 A170309 A170357

Adjacent sequences: A170210 A170211 A170212 * A170214 A170215 A170216

Keyword

nonn

Author

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

Status

approved