A166723 Number of reduced words of length n in Coxeter group on 44 generators S_i with relations (S_i)^2 = (S_i S_j)^12 = I.

1, 44, 1892, 81356, 3498308, 150427244, 6468371492, 278139974156, 11960018888708, 514280812214444, 22114074925221092, 950905221784506956, 40888924536733798162, 1758223755079553280288, 75603621468420789304176

Offset

0,2

Comments

The initial terms coincide with those of A170763, 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 (42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, -903).

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)/(903*t^12 - 42*t^11 - 42*t^10 - 42*t^9 -42*t^8 -42*t^7 -42*t^6 - 42*t^5 - 42*t^4 - 42*t^3 - 42*t^2 - 42*t + 1).

Mathematica

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)/(903*t^12 - 42*t^11 - 42*t^10 - 42*t^9 - 42*t^8 - 42*t^7 - 42*t^6 - 42*t^5 - 42*t^4 - 42*t^3 - 42*t^2 - 42*t + 1), {t, 0, 50}], t] (* G. C. Greubel, May 24 2016 *)
coxG[{12, 903, -42}] (* The coxG program is at A169452 *) (* Harvey P. Dale, Aug 03 2023 *)

Prog

(PARI) Vec((1+x^4+x^8)*(1+x^2)*(1+x)^2/(1-42*x-42*x^2-42*x^3-42*x^4-42*x^5-42*x^6-42*x^7-42*x^8-42*x^9-42*x^10-42*x^11+903*x^12)+O(x^99)) \\ Charles R Greathouse IV, Jun 08 2026

Crossrefs

Cf. A170763, A154638.

Sequence in context: A165695 A166254 A166438 * A167097 A167641 A167854

Adjacent sequences: A166720 A166721 A166722 * A166724 A166725 A166726

Keyword

nonn,easy

Author

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

Status

approved