A166617 Number of reduced words of length n in Coxeter group on 30 generators S_i with relations (S_i)^2 = (S_i S_j)^12 = I.

1, 30, 870, 25230, 731670, 21218430, 615334470, 17844699630, 517496289270, 15007392388830, 435214379276070, 12621216999006030, 366015292971174435, 10614443496164046000, 307818861388756968600, 8926746980273941492800

Offset

0,2

Comments

The initial terms coincide with those of A170749, 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 (28, 28, 28, 28, 28, 28, 28, 28, 28, 28, 28, -406).

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)/(406*t^12 - 28*t^11 - 28*t^10 - 28*t^9 -28*t^8 -28*t^7 - 28*t^6 - 28*t^5 - 28*t^4 - 28*t^3 - 28*t^2 - 28*t +1).

Mathematica

coxG[{12, 406, -28}] (* The coxG program is at A169452 *) (* Harvey P. Dale, Jan 21 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)/(406*t^12 - 28*t^11 - 28*t^10 - 28*t^9 - 28*t^8 - 28*t^7 - 28*t^6 - 28*t^5 - 28*t^4 - 28*t^3 - 28*t^2 - 28*t + 1), {t, 0, 50}], t] (* G. C. Greubel, May 19 2016 *)

Crossrefs

Sequence in context: A165515 A166026 A166424 * A167083 A167370 A167715

Adjacent sequences: A166614 A166615 A166616 * A166618 A166619 A166620

Keyword

nonn

Author

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

Status

approved