A167959 Number of reduced words of length n in Coxeter group on 43 generators S_i with relations (S_i)^2 = (S_i S_j)^16 = I.

1, 43, 1806, 75852, 3185784, 133802928, 5619722976, 236028364992, 9913191329664, 416354035845888, 17486869505527296, 734448519232146432, 30846837807750150144, 1295567187925506306048, 54413821892871264854016

Offset

0,2

Comments

The initial terms coincide with those of A170762, 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 (41,41,41,41,41,41,41,41,41,41, 41,41,41,41,41,-861).

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)/( 861*t^16 - 41*t^15 - 41*t^14 - 41*t^13 - 41*t^12 - 41*t^11 - 41*t^10 - 41*t^9 - 41*t^8 - 41*t^7 - 41*t^6 - 41*t^5 - 41*t^4 - 41*t^3 - 41*t^2 - 41*t + 1).

From G. C. Greubel, Apr 27 2023: (Start)

G.f.: (1 + x)*(1 + x^16)/(1 - 42*x + 861*x^16 - 820*x^17).

a(n) = 41*Sum_{k=1..15} a(n-k) - 861*a(n-16). (End)

Mathematica

CoefficientList[Series[(1+x)*(1+x^16)/(1-42*x+861*x^16-820*x^17), {x, 0, 50}], x] (* G. C. Greubel, Jul 02 2016; Apr 27 2023 *)
coxG[{16, 861, -41, 40}] (* The coxG program is at A169452 *) (* G. C. Greubel, Apr 27 2023 *)

Prog

(Magma) R<x>:=PowerSeriesRing(Integers(), 40); Coefficients(R!( (1+x)*(1+x^16)/(1-42*x+861*x^16-820*x^17) )); // G. C. Greubel, Apr 27 2023
(SageMath)
def A167959_list(prec):
    P.<x> = PowerSeriesRing(ZZ, prec)
    return P( (1+x)*(1+x^16)/(1-42*x+861*x^16-820*x^17) ).list()
A167959_list(40) # G. C. Greubel, Apr 27 2023

Crossrefs

Cf. A154638, A169452, A170762.

Sequence in context: A167096 A167640 A167849 * A168720 A168768 A168816

Adjacent sequences: A167956 A167957 A167958 * A167960 A167961 A167962

Keyword

nonn

Author

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

Status

approved