A166716 Number of reduced words of length n in Coxeter group on 42 generators S_i with relations (S_i)^2 = (S_i S_j)^12 = I.

1, 42, 1722, 70602, 2894682, 118681962, 4865960442, 199504378122, 8179679503002, 335366859623082, 13750041244546362, 563751691026400842, 23113819332082433661, 947666592615379744800, 38854330297230568090320

Offset

0,2

Comments

The initial terms coincide with those of A170761, although the two sequences are eventually different.

Computed with MAGMA using commands similar to those used to compute A154638.

Links

G. C. Greubel, Table of n, a(n) for n = 0..500

Index entries for linear recurrences with constant coefficients, signature (40, 40, 40, 40, 40, 40, 40, 40, 40, 40, 40, -820).

Formula

G.f.: (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)/(820*t^12 - 40*t^11 - 40*t^10 - 40*t^9 -40*t^8 -40*t^7 -40*t^6 - 40*t^5 - 40*t^4 - 40*t^3 - 40*t^2 - 40*t + 1).

Mathematica

coxG[{12, 820, -40}] (* The coxG program is at A169452 *) (* Harvey P. Dale, Jan 16 2015 *)
CoefficientList[Series[(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)/(820*t^12 - 40*t^11 - 40*t^10 - 40*t^9 - 40*t^8 - 40*t^7 - 40*t^6 - 40*t^5 - 40*t^4 - 40*t^3 - 40*t^2 - 40*t + 1), {t, 0, 50}], t] (* G. C. Greubel, May 24 2016 *)

Crossrefs

Sequence in context: A165693 A166230 A166436 * A167095 A167599 A167848

Adjacent sequences: A166713 A166714 A166715 * A166717 A166718 A166719

Keyword

nonn

Author

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

Status

approved