A168763 Number of reduced words of length n in Coxeter group on 38 generators S_i with relations (S_i)^2 = (S_i S_j)^18 = I.

1, 38, 1406, 52022, 1924814, 71218118, 2635070366, 97497603542, 3607411331054, 133474219248998, 4938546112212926, 182726206151878262, 6760869627619495694, 250152176221921340678, 9255630520211089605086

Offset

0,2

Comments

The initial terms coincide with those of A170757, although the two sequences are eventually different.

First disagreement at index 18: a(18) = 17346541751389335905357582143, A170757(18) = 17346541751389335905357582846. - Klaus Brockhaus, Mar 26 2011

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 (36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, 36, -666).

Formula

G.f.: (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)/(666*t^18 - 36*t^17 - 36*t^16 - 36*t^15 - 36*t^14 - 36*t^13 - 36*t^12 - 36*t^11 - 36*t^10 - 36*t^9 - 36*t^8 - 36*t^7 - 36*t^6 - 36*t^5 - 36*t^4 - 36*t^3 - 36*t^2 - 36*t + 1).

Mathematica

CoefficientList[Series[(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)/(666*t^18 - 36*t^17 - 36*t^16 - 36*t^15 - 36*t^14 - 36*t^13 - 36*t^12 - 36*t^11 - 36*t^10 - 36*t^9 - 36*t^8 - 36*t^7 - 36*t^6 - 36*t^5 - 36*t^4 - 36*t^3 - 36*t^2 - 36*t + 1), {t, 0, 50}], t] (* G. C. Greubel, Aug 11 2016 *)
coxG[{18, 666, -36}] (* The coxG program is at A169452 *) (* Harvey P. Dale, Oct 21 2016 *)

Crossrefs

Cf. A170757 (G.f.: (1+x)/(1-37*x)).

Sequence in context: A167827 A167954 A168715 * A168811 A168859 A168907

Adjacent sequences: A168760 A168761 A168762 * A168764 A168765 A168766

Keyword

nonn,easy

Author

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

Status

approved