A167954 Number of reduced words of length n in Coxeter group on 38 generators S_i with relations (S_i)^2 = (S_i S_j)^16 = 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.

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,-666).

Formula

G.f.: (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^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).

From G. C. Greubel, Sep 06 2023: (Start)

G.f.: (1+t)*(1-t^16)/(1 - 37*t + 702*t^16 - 666*t^17).

a(n) = 36*Sum_{j=1..15} a(n-j) - 666*a(n-16). (End)

Mathematica

CoefficientList[Series[(1+t)*(1-t^16)/(1-37*t+702*t^16-666*t^17), {t, 0, 50}], t] (* G. C. Greubel, Jul 02 2016 *)
coxG[{16, 666, -36, 40}] (* The coxG program is at A169452 *) (* G. C. Greubel, Sep 06 2023 *)

Prog

(Magma) R<x>:=PowerSeriesRing(Integers(), 40); Coefficients(R!( (1+x)*(1-x^16)/(1-37*x+702*x^16-666*x^17) )); // G. C. Greubel, Sep 06 2023
(SageMath)
def A167955_list(prec):
    P.<x> = PowerSeriesRing(ZZ, prec)
    return P( (1+x)*(1-x^16)/(1-37*x+702*x^16-666*x^17) ).list()
A167955_list(40) # G. C. Greubel, Sep 06 2023

Crossrefs

Cf. A154638, A169452, A170757.

Sequence in context: A167091 A167492 A167827 * A168715 A168763 A168811

Adjacent sequences: A167951 A167952 A167953 * A167955 A167956 A167957

Keyword

nonn

Author

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

Status

approved