A169361 Number of reduced words of length n in Coxeter group on 12 generators S_i with relations (S_i)^2 = (S_i S_j)^31 = 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.

First disagreement at index 31: a(31) = 209392827226636887822705645045546, A003954(31) = 209392827226636887822705645045612. - Klaus Brockhaus, Jun 17 2011

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, -55).

Formula

G.f.: (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^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[{31, 55, -10}] (* The coxG program is at A169452 *) (* Harvey P. Dale, Dec 17 2021 *)

Crossrefs

Cf. A003954 (G.f.: (1+x)/(1-11*x)).

Sequence in context: A169217 A169265 A169313 * A169409 A169457 A169505

Adjacent sequences: A169358 A169359 A169360 * A169362 A169363 A169364

Keyword

nonn

Author

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

Status

approved