A170763 -id:A170763 - cp's OEIS frontend

A167854 Number of reduced words of length n in Coxeter group on 44 generators S_i with relations (S_i)^2 = (S_i S_j)^15 = I.

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

Offset: 0

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

nonn

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.

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, -903).

CoefficientList[Series[(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^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), {t, 0, 50}], t] (* G. C. Greubel, Jun 28 2016 *)
coxG[{15,903,-42}] (* The coxG program is at A169452 *) (* Harvey P. Dale, Oct 04 2017 *)

G.f.: (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^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).

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.

Original entry on oeis.org

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

Offset: 0

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

nonn

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.

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).

Cf. A154638, A169452, A170763.

R:=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

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 *)

def A167960_list(prec):
    P. = 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

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)

A168721 Number of reduced words of length n in Coxeter group on 44 generators S_i with relations (S_i)^2 = (S_i S_j)^17 = I.

Original entry on oeis.org

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

Offset: 0

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

nonn

The initial terms coincide with those of A170763, although the two sequences are eventually different.
First disagreement at index 17: a(17) = 6011017132089732112341867898, A170763(17) = 6011017132089732112341868844. - Klaus Brockhaus, Mar 28 2011
Computed with MAGMA using commands similar to those used to compute A154638.

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, 42, -903).

Cf. A170763 (G.f.: (1+x)/(1-43*x)).

coxG[{17,903,-42}] (* The coxG program is at A169452 *) (* Harvey P. Dale, Feb 27 2015 *)
CoefficientList[Series[(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)/(903*t^17 - 42*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), {t,0,50}], t] (* G. C. Greubel, Aug 06 2016 *)

G.f.: (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)/(903*t^17 - 42*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).

A168769 Number of reduced words of length n in Coxeter group on 44 generators S_i with relations (S_i)^2 = (S_i S_j)^18 = I.

Original entry on oeis.org

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

Offset: 0

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

The initial terms coincide with those of A170763, although the two sequences are eventually different.
First disagreement at index 18: a(18) = 258473736679858480830700359346, A170763(18) = 258473736679858480830700360292. - Klaus Brockhaus, Mar 26 2011
Computed with MAGMA using commands similar to those used to compute A154638.

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, 42, 42, -903).

Cf. A170763 (G.f.: (1+x)/(1-43*x)).

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)/(903*t^18 - 42*t^17 - 42*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), {t, 0, 50}], t] (* G. C. Greubel, Aug 11 2016 *)

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)/(903*t^18 - 42*t^17 - 42*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).

A168817 Number of reduced words of length n in Coxeter group on 44 generators S_i with relations (S_i)^2 = (S_i S_j)^19 = I.

Original entry on oeis.org

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

Offset: 0

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

The initial terms coincide with those of A170763, although the two sequences are eventually different.
First disagreement at index 19: a(19) = 11114370677233914675720115491610, A170763(19) = 11114370677233914675720115492556. - Klaus Brockhaus, Apr 01 2011
Computed with MAGMA using commands similar to those used to compute A154638.

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, 42, 42, 42, -903).

Cf. A170763 (G.f.: (1+x)/(1-43*x)).

CoefficientList[Series[(t^19 + 2*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)/(903*t^19 - 42*t^18 - 42*t^17 - 42*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), {t,0,50}], t] (* G. C. Greubel, Nov 21 2016 *)

G.f.: (t^19 + 2*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)/(903*t^19 - 42*t^18 - 42*t^17 - 42*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).

A169345 Number of reduced words of length n in Coxeter group on 44 generators S_i with relations (S_i)^2 = (S_i S_j)^30 = I.

Original entry on oeis.org

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

Offset: 0

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

nonn

The initial terms coincide with those of A170763, although the two sequences are eventually different.
First disagreement at index 30: a(30) = 10328515088516010583734507189289051903638876668146, A170763(30) = 10328515088516010583734507189289051903638876669092. - Klaus Brockhaus, Jun 23 2011
Computed with Magma using commands similar to those used to compute A154638.

Robert Israel, Table of n, a(n) for n = 0..600
Index entries for linear recurrences with constant coefficients, signature (42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, -903).

Cf. A170763 (g.f.: (1+x)/(1-43*x)).

g:= (t^30 + 2*t^29 + 2*t^28 + 2*t^27 + 2*t^26 + 2*t^25 + 2*t^24 + 2*t^23 + 2*t^22 + 2*t^21 + 2*t^20 + 2*t^19 + 2*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)/(903*t^30 - 42*t^29 - 42*t^28 - 42*t^27 - 42*t^26 - 42*t^25 - 42*t^24 - 42*t^23 - 42*t^22 - 42*t^21 - 42*t^20 - 42*t^19 - 42*t^18 - 42*t^17 - 42*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):
S:= series(g,t,101):
seq(coeff(S,t,j),j=0..100); # Robert Israel, Nov 23 2015

coxG[{30,903,-42}] (* The coxG program is at A169452 *) (* Harvey P. Dale, Jan 25 2015 *)

G.f.: (t^30 + 2*t^29 + 2*t^28 + 2*t^27 + 2*t^26 + 2*t^25 + 2*t^24 + 2*t^23 + 2*t^22 + 2*t^21 + 2*t^20 + 2*t^19 + 2*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)/(903*t^30 - 42*t^29 - 42*t^28 - 42*t^27 - 42*t^26 - 42*t^25 - 42*t^24 - 42*t^23 - 42*t^22 - 42*t^21 - 42*t^20 - 42*t^19 - 42*t^18 - 42*t^17 - 42*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).

A170725 Number of reduced words of length n in Coxeter group on 44 generators S_i with relations (S_i)^2 = (S_i S_j)^50 = I.

Original entry on oeis.org

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

Offset: 0

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

The initial terms coincide with those of A170763, although the two sequences are eventually different.

The first disagreement is at index 50 and the difference is 946. - Vincenzo Librandi, Dec 07 2012

Georg Fischer, Table of n, a(n) for n = 0..200 (first 50 terms from Vincenzo Librandi)
Index entries for linear recurrences with constant coefficients, signature (42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, 42, -903).

With[{num=Total[2t^Range[49]]+t^50+1,den=Total[-42 t^Range[49]]+ 903t^50+ 1}, CoefficientList[Series[num/den,{t,0,30}],t]] (* Harvey P. Dale, Mar 02 2012 *)

G.f. (t^50 + 2*t^49 + 2*t^48 + 2*t^47 + 2*t^46 + 2*t^45 + 2*t^44 + 2*t^43 +
2*t^42 + 2*t^41 + 2*t^40 + 2*t^39 + 2*t^38 + 2*t^37 + 2*t^36 + 2*t^35 +
2*t^34 + 2*t^33 + 2*t^32 + 2*t^31 + 2*t^30 + 2*t^29 + 2*t^28 + 2*t^27 +
2*t^26 + 2*t^25 + 2*t^24 + 2*t^23 + 2*t^22 + 2*t^21 + 2*t^20 + 2*t^19 +
2*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)/(903*t^50 - 42*t^49 - 42*t^48 - 42*t^47 - 42*t^46 - 42*t^45 -
42*t^44 - 42*t^43 - 42*t^42 - 42*t^41 - 42*t^40 - 42*t^39 - 42*t^38 -
42*t^37 - 42*t^36 - 42*t^35 - 42*t^34 - 42*t^33 - 42*t^32 - 42*t^31 -
42*t^30 - 42*t^29 - 42*t^28 - 42*t^27 - 42*t^26 - 42*t^25 - 42*t^24 -
42*t^23 - 42*t^22 - 42*t^21 - 42*t^20 - 42*t^19 - 42*t^18 - 42*t^17 -
42*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)

A164688 Number of reduced words of length n in Coxeter group on 44 generators S_i with relations (S_i)^2 = (S_i S_j)^7 = I.

Original entry on oeis.org

1, 44, 1892, 81356, 3498308, 150427244, 6468371492, 278139973210, 11960018807352, 514280806967928, 22114074624447960, 950905205618825688, 40888923702614731128, 1758223713235658179896, 75603619412131966509354

Offset: 0

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

nonn

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.

Index entries for linear recurrences with constant coefficients, signature (42, 42, 42, 42, 42, 42, -903).

G.f.: (t^7 + 2*t^6 + 2*t^5 + 2*t^4 + 2*t^3 + 2*t^2 + 2*t + 1)/(903*t^7 - 42*t^6 - 42*t^5 - 42*t^4 - 42*t^3 - 42*t^2 - 42*t + 1).

A165176 Number of reduced words of length n in Coxeter group on 44 generators S_i with relations (S_i)^2 = (S_i S_j)^8 = I.

Original entry on oeis.org

1, 44, 1892, 81356, 3498308, 150427244, 6468371492, 278139974156, 11960018887762, 514280812133088, 22114074919974576, 950905221483733824, 40888924520568117840, 1758223754245434293664, 75603621426576899368944

Offset: 0

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

nonn

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.

Index entries for linear recurrences with constant coefficients, signature (42, 42, 42, 42, 42, 42, 42, -903).

coxG[{8,903,-42}] (* The coxG program is at A169452 *) (* Harvey P. Dale, May 27 2019 *)

G.f. (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^8 -

42*t^7 - 42*t^6 - 42*t^5 - 42*t^4 - 42*t^3 - 42*t^2 - 42*t + 1)

A165695 Number of reduced words of length n in Coxeter group on 44 generators S_i with relations (S_i)^2 = (S_i S_j)^9 = I.

Original entry on oeis.org

1, 44, 1892, 81356, 3498308, 150427244, 6468371492, 278139974156, 11960018888708, 514280812213498, 22114074925139736, 950905221779260440, 40888924536433025976, 1758223755063387680376, 75603621467586675482712

Offset: 0

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

nonn

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.

Index entries for linear recurrences with constant coefficients, signature (42, 42, 42, 42, 42, 42, 42, 42, -903).

coxG[{9,903,-42}] (* The coxG program is at A169452 *) (* Harvey P. Dale, Mar 08 2020 *)

G.f. (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^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)

cp's OEIS Frontend

A167854 Number of reduced words of length n in Coxeter group on 44 generators S_i with relations (S_i)^2 = (S_i S_j)^15 = I.

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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.

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A168721 Number of reduced words of length n in Coxeter group on 44 generators S_i with relations (S_i)^2 = (S_i S_j)^17 = I.

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A168769 Number of reduced words of length n in Coxeter group on 44 generators S_i with relations (S_i)^2 = (S_i S_j)^18 = I.

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A168817 Number of reduced words of length n in Coxeter group on 44 generators S_i with relations (S_i)^2 = (S_i S_j)^19 = I.

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A169345 Number of reduced words of length n in Coxeter group on 44 generators S_i with relations (S_i)^2 = (S_i S_j)^30 = I.

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A170725 Number of reduced words of length n in Coxeter group on 44 generators S_i with relations (S_i)^2 = (S_i S_j)^50 = I.

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A164688 Number of reduced words of length n in Coxeter group on 44 generators S_i with relations (S_i)^2 = (S_i S_j)^7 = I.

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A165176 Number of reduced words of length n in Coxeter group on 44 generators S_i with relations (S_i)^2 = (S_i S_j)^8 = I.