A167960 Number of reduced words of length n in Coxeter group on 44 generators S_i with relations (S_i)^2 = (S_i S_j)^16 = I.

1, 44, 1892, 81356, 3498308, 150427244, 6468371492, 278139974156, 11960018888708, 514280812214444, 22114074925221092, 950905221784506956, 40888924536733799108, 1758223755079553361644, 75603621468420794550692

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 (42,42,42,42,42,42,42,42,42,42,42,42,42,42,42,-903).

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)/( 903*t^16 - 42*t^15 - 42*t^14 - 42*t^13 - 42*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).

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

G.f.: (1 + x)*(1 + x^16)/(1 - 43*x + 903*x^16 - 861*x^17).

a(n) = 42*Sum_{k=1..m-1} a(n-k) - 903*a(n-m). (End)

Mathematica

CoefficientList[Series[(1+x)*(1+x^16)/(1-43*x+903*x^16-861*x^17), {x, 0, 50}], x] (* G. C. Greubel, Jul 02 2016; Apr 27 2023 *)
coxG[{16, 903, -42}] (* The coxG program is at A169452 *) (* Harvey P. Dale, Jul 19 2021 *)

Prog

(Magma) R<x>:=PowerSeriesRing(Integers(), 40); Coefficients(R!( (1+x)*(1+x^16)/(1-43*x+903*x^16-861*x^17) )); // G. C. Greubel, Apr 27 2023
(SageMath)
def A167960_list(prec):
    P.<x> = PowerSeriesRing(ZZ, prec)
    return P( (1+x)*(1+x^16)/(1-43*x+903*x^16-861*x^17) ).list()
A167960_list(40) # G. C. Greubel, Apr 27 2023

Crossrefs

Cf. A154638, A169452, A170763.

Sequence in context: A167097 A167641 A167854 * A168721 A168769 A168817

Adjacent sequences: A167957 A167958 A167959 * A167961 A167962 A167963

Keyword

nonn

Author

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

Status

approved