A003950 -id:A003950 - cp's OEIS frontend

A168685 Number of reduced words of length n in Coxeter group on 8 generators S_i with relations (S_i)^2 = (S_i S_j)^17 = I.

1, 8, 56, 392, 2744, 19208, 134456, 941192, 6588344, 46118408, 322828856, 2259801992, 15818613944, 110730297608, 775112083256, 5425784582792, 37980492079544, 265863444556780, 1861044111897264, 13027308783279504

Offset: 0

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

nonn

The initial terms coincide with those of A003950, although the two sequences are eventually different.
First disagreement at index 17: a(17) = 265863444556780, A003950(17) = 265863444556808. - Klaus Brockhaus, Mar 30 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 (6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,-21).

Cf. A003950 (g.f.: (1+x)/(1-7*x)).

R:=PowerSeriesRing(Integers(), 40);
Coefficients(R!( (1+t)*(1-t^17)/(1 -7*t +27*t^17 -21*t^18) )); // G. C. Greubel, Mar 24 2021

CoefficientList[Series[(1+t)*(1-t^17)/(1 -7*t +27*t^17 -21*t^18), {t, 0, 40}], t] (* G. C. Greubel, Aug 03 2016; Mar 24 2021 *)
coxG[{17, 21, -6, 40}] (* The coxG program is at A169452 *) (* G. C. Greubel, Mar 24 2021 *)

def A168685_list(prec):
    P. = PowerSeriesRing(ZZ, prec)
    return P( (1+t)*(1-t^17)/(1 -7*t +27*t^17 -21*t^18) ).list()
A168685_list(40) # G. C. Greubel, Mar 24 2021

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)/ (21*t^17 - 6*t^16 - 6*t^15 - 6*t^14 - 6*t^13 - 6*t^12 - 6*t^11 - 6*t^10 - 6*t^9 - 6*t^8 - 6*t^7 - 6*t^6 - 6*t^5 - 6*t^4 - 6*t^3 - 6*t^2 - 6*t + 1).

G.f.: (1+t)*(1-t^17)/(1 - 7*t + 27*t^17 - 21*t^18). - G. C. Greubel, Mar 24 2021

A168733 Number of reduced words of length n in Coxeter group on 8 generators S_i with relations (S_i)^2 = (S_i S_j)^18 = I.

Original entry on oeis.org

1, 8, 56, 392, 2744, 19208, 134456, 941192, 6588344, 46118408, 322828856, 2259801992, 15818613944, 110730297608, 775112083256, 5425784582792, 37980492079544, 265863444556808, 1861044111897628, 13027308783283200

Offset: 0

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

The initial terms coincide with those of A003950, although the two sequences are eventually different.
First disagreement at index 18: a(18) = 1861044111897628, A003950(18) = 1861044111897656. - Klaus Brockhaus, Mar 27 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 (6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, -21).

Cf. A003950 (G.f.: (1+x)/(1-7*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)/(21*t^18 - 6*t^17 - 6*t^16 - 6*t^15 - 6*t^14 - 6*t^13 - 6*t^12 - 6*t^11 - 6*t^10 - 6*t^9 - 6*t^8 - 6*t^7 - 6*t^6 - 6*t^5 - 6*t^4 - 6*t^3 - 6*t^2 - 6*t + 1), {t,0,50}], t] (* G. C. Greubel, Aug 06 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)/(21*t^18 - 6*t^17 - 6*t^16 - 6*t^15 - 6*t^14 - 6*t^13 - 6*t^12 - 6*t^11 - 6*t^10 - 6*t^9 - 6*t^8 - 6*t^7 - 6*t^6 - 6*t^5 - 6*t^4 - 6*t^3 - 6*t^2 - 6*t + 1).

A168781 Number of reduced words of length n in Coxeter group on 8 generators S_i with relations (S_i)^2 = (S_i S_j)^19 = I.

Original entry on oeis.org

1, 8, 56, 392, 2744, 19208, 134456, 941192, 6588344, 46118408, 322828856, 2259801992, 15818613944, 110730297608, 775112083256, 5425784582792, 37980492079544, 265863444556808, 1861044111897656, 13027308783283564

Offset: 0

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

The initial terms coincide with those of A003950, although the two sequences are eventually different.
First disagreement at index 19: a(19) = 13027308783283564, A003950(19) = 13027308783283592. - Klaus Brockhaus, Mar 25 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 (6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, -21).

Cf. A003950 (G.f.: (1+x)/(1-7*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)/(21*t^19 - 6*t^18 - 6*t^17 - 6*t^16 - 6*t^15 - 6*t^14 - 6*t^13 - 6*t^12 - 6*t^11 - 6*t^10 - 6*t^9 - 6*t^8 - 6*t^7 - 6*t^6 - 6*t^5 - 6*t^4 - 6*t^3 - 6*t^2 - 6*t + 1), {t, 0, 50}], t] (* G. C. Greubel, Aug 12 2016 *)
coxG[{19,21,-6}] (* The coxG program is at A169452 *) (* Harvey P. Dale, Oct 02 2024 *)

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)/(21*t^19 - 6*t^18 - 6*t^17 - 6*t^16 - 6*t^15 - 6*t^14 - 6*t^13 - 6*t^12 - 6*t^11 - 6*t^10 - 6*t^9 - 6*t^8 - 6*t^7 - 6*t^6 - 6*t^5 - 6*t^4 - 6*t^3 - 6*t^2 - 6*t + 1).

A168829 Number of reduced words of length n in Coxeter group on 8 generators S_i with relations (S_i)^2 = (S_i S_j)^20 = I.

Original entry on oeis.org

1, 8, 56, 392, 2744, 19208, 134456, 941192, 6588344, 46118408, 322828856, 2259801992, 15818613944, 110730297608, 775112083256, 5425784582792, 37980492079544, 265863444556808, 1861044111897656, 13027308783283592

Offset: 0

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

nonn

The initial terms coincide with those of A003950, although the two sequences are eventually different.
First disagreement at index 20: a(20) = 91191161482985116, A003950(20) = 91191161482985144. - 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..1000
Index entries for linear recurrences with constant coefficients, signature (6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, -21).

Cf. A003950 (G.f.: (1+x)/(1-7*x)).

CoefficientList[Series[(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)/(21*t^20 - 6*t^19 - 6*t^18 - 6*t^17 - 6*t^16 - 6*t^15 - 6*t^14 - 6*t^13 - 6*t^12 - 6*t^11 - 6*t^10 - 6*t^9 - 6*t^8 - 6*t^7 - 6*t^6 - 6*t^5 - 6*t^4 - 6*t^3 - 6*t^2 - 6*t + 1), {t,0,100}], t] (* G. C. Greubel, Nov 22 2016 *)

G.f.: (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)/(21*t^20 - 6*t^19 - 6*t^18 - 6*t^17 - 6*t^16 - 6*t^15 - 6*t^14 - 6*t^13 - 6*t^12 - 6*t^11 - 6*t^10 - 6*t^9 - 6*t^8 - 6*t^7 - 6*t^6 - 6*t^5 - 6*t^4 - 6*t^3 - 6*t^2 - 6*t + 1).

A169213 Number of reduced words of length n in Coxeter group on 8 generators S_i with relations (S_i)^2 = (S_i S_j)^28 = I.

Original entry on oeis.org

1, 8, 56, 392, 2744, 19208, 134456, 941192, 6588344, 46118408, 322828856, 2259801992, 15818613944, 110730297608, 775112083256, 5425784582792, 37980492079544, 265863444556808, 1861044111897656, 13027308783283592

Offset: 0

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

nonn

The initial terms coincide with those of A003950, although the two sequences are eventually different.
First disagreement at index 28: a(28) = 525698898908274241116316, A003950(28) = 525698898908274241116344. - Klaus Brockhaus, May 24 2011
Computed with Magma using commands similar to those used to compute A154638.

Vincenzo Librandi, Table of n, a(n) for n = 0..200
Index entries for linear recurrences with constant coefficients, signature (6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, -21).

Cf. A003950 (G.f.: (1+x)/(1-7*x)).

With[{num=Total[2t^Range[27]]+t^28+1,den=Total[-6 t^Range[27]]+21t^28+ 1},CoefficientList[Series[num/den,{t,0,30}],t]] (* Harvey P. Dale, Feb 10 2014 *)

G.f.: (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)/(21*t^28 - 6*t^27 - 6*t^26 - 6*t^25 - 6*t^24 - 6*t^23 - 6*t^22 - 6*t^21 - 6*t^20 - 6*t^19 - 6*t^18 - 6*t^17 - 6*t^16 - 6*t^15 - 6*t^14 - 6*t^13 - 6*t^12 - 6*t^11 - 6*t^10 - 6*t^9 - 6*t^8 - 6*t^7 - 6*t^6 - 6*t^5 - 6*t^4 - 6*t^3 - 6*t^2 - 6*t + 1).

A169357 Number of reduced words of length n in Coxeter group on 8 generators S_i with relations (S_i)^2 = (S_i S_j)^31 = I.

Original entry on oeis.org

1, 8, 56, 392, 2744, 19208, 134456, 941192, 6588344, 46118408, 322828856, 2259801992, 15818613944, 110730297608, 775112083256, 5425784582792, 37980492079544, 265863444556808, 1861044111897656, 13027308783283592

Offset: 0

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

The initial terms coincide with those of A003950, although the two sequences are eventually different.
First disagreement at index 31: a(31) = 180314722325538064702905964, A003950(31) = 180314722325538064702905992. - Klaus Brockhaus, Jun 17 2011
Computed with Magma using commands similar to those used to compute A154638.

Vincenzo Librandi, Table of n, a(n) for n = 0..200
Index entries for linear recurrences with constant coefficients, signature (6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,-21).

Cf. A003950 (G.f.: (1+x)/(1-7*x)).

With[{num=Total[2t^Range[30]]+t^31+1,den=Total[-6 t^Range[30]]+21t^31+ 1},CoefficientList[Series[num/den,{t,0,30}],t]] (* Harvey P. Dale, Sep 17 2013 *)

G.f.: (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)/(21*t^31 - 6*t^30 - 6*t^29 - 6*t^28 - 6*t^27 - 6*t^26 - 6*t^25 - 6*t^24 - 6*t^23 - 6*t^22 - 6*t^21 - 6*t^20 - 6*t^19 - 6*t^18 - 6*t^17 - 6*t^16 - 6*t^15 - 6*t^14 - 6*t^13 - 6*t^12 - 6*t^11 - 6*t^10 - 6*t^9 - 6*t^8 - 6*t^7 - 6*t^6 - 6*t^5 - 6*t^4 - 6*t^3 - 6*t^2 - 6*t + 1).

A169405 Number of reduced words of length n in Coxeter group on 8 generators S_i with relations (S_i)^2 = (S_i S_j)^32 = I.

Original entry on oeis.org

1, 8, 56, 392, 2744, 19208, 134456, 941192, 6588344, 46118408, 322828856, 2259801992, 15818613944, 110730297608, 775112083256, 5425784582792, 37980492079544, 265863444556808, 1861044111897656, 13027308783283592

Offset: 0

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

The initial terms coincide with those of A003950, although the two sequences are eventually different.
First disagreement is at index 32, the difference is 28. - Klaus Brockhaus, Jun 26 2011
Computed with Magma using commands similar to those used to compute A154638.

Vincenzo Librandi, Table of n, a(n) for n = 0..500
Index entries for linear recurrences with constant coefficients, signature (6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, -21).

Cf. A003950 (G.f.: (1+x)/(1-7*x) ).

With[{num=Total[2t^Range[31]]+t^32+1,den=Total[-6 t^Range[31]]+21t^32+1}, CoefficientList[Series[num/den,{t,0,30}],t]] (* Harvey P. Dale, Jan 27 2012 *)

x='x+O('x^66); /* that many terms */
Vec((1+2*sum(k=1,31,x^k)+x^32)/(1-6*sum(k=1,31,x^k)+21*x^32))   /* show terms */
/* Joerg Arndt, Jun 26 2011 */

G.f.: (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)/(21*t^32 - 6*t^31 - 6*t^30 - 6*t^29 - 6*t^28 - 6*t^27 - 6*t^26 - 6*t^25 - 6*t^24 - 6*t^23 - 6*t^22 - 6*t^21 - 6*t^20 - 6*t^19 - 6*t^18 - 6*t^17 - 6*t^16 - 6*t^15 - 6*t^14 - 6*t^13 - 6*t^12 - 6*t^11 - 6*t^10 - 6*t^9 - 6*t^8 - 6*t^7 - 6*t^6 - 6*t^5 - 6*t^4 - 6*t^3 - 6*t^2 - 6*t + 1).

G.f.: (1+2*sum(k=1..31,x^k)+x^32)/(1-6*sum(k=1..31,x^k)+21*x^32).

A170689 Number of reduced words of length n in Coxeter group on 8 generators S_i with relations (S_i)^2 = (S_i S_j)^50 = I.

Original entry on oeis.org

1, 8, 56, 392, 2744, 19208, 134456, 941192, 6588344, 46118408, 322828856, 2259801992, 15818613944, 110730297608, 775112083256, 5425784582792, 37980492079544, 265863444556808, 1861044111897656, 13027308783283592

Offset: 0

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

nonn

The initial terms coincide with those of A003950, although the two sequences are eventually different.
Computed with MAGMA using commands similar to those used to compute A154638.
About the initial comment, first disagreement is at index 50 and the difference is 28.  - Vincenzo Librandi, Dec 09 2012

Vincenzo Librandi, Table of n, a(n) for n = 0..200
Index entries for linear recurrences with constant coefficients, signature (6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, -21).

With[{num = Total[2 t^Range[49]] + t^50 + 1, den = Total[-6 t^Range[49]] + 21 t^50 + 1}, CoefficientList[Series[num/den, {t, 0, 40}], t]] (* Vincenzo Librandi, Dec 09 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)/(21*t^50 - 6*t^49 - 6*t^48 - 6*t^47 - 6*t^46 - 6*t^45 - 6*t^44
- 6*t^43 - 6*t^42 - 6*t^41 - 6*t^40 - 6*t^39 - 6*t^38 - 6*t^37 - 6*t^36
- 6*t^35 - 6*t^34 - 6*t^33 - 6*t^32 - 6*t^31 - 6*t^30 - 6*t^29 - 6*t^28
- 6*t^27 - 6*t^26 - 6*t^25 - 6*t^24 - 6*t^23 - 6*t^22 - 6*t^21 - 6*t^20
- 6*t^19 - 6*t^18 - 6*t^17 - 6*t^16 - 6*t^15 - 6*t^14 - 6*t^13 - 6*t^12
- 6*t^11 - 6*t^10 - 6*t^9 - 6*t^8 - 6*t^7 - 6*t^6 - 6*t^5 - 6*t^4 -
6*t^3 - 6*t^2 - 6*t + 1).

A162754 Number of reduced words of length n in Coxeter group on 8 generators S_i with relations (S_i)^2 = (S_i S_j)^3 = I.

Original entry on oeis.org

1, 8, 56, 364, 2352, 15120, 97188, 624456, 4012344, 25779852, 165639600, 1064257488, 6838005636, 43935147144, 282289509432, 1813749821100, 11653597893168, 74876006587536, 481088880641124, 3091063767615432

Offset: 0

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

nonn

The initial terms coincide with those of A003950, 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 (6, 6, -21).

coxG[{3,21,-6}] (* The coxG program is at A169452 *) (* Harvey P. Dale, Mar 23 2025 *)

G.f.: (t^3 + 2*t^2 + 2*t + 1)/(21*t^3 - 6*t^2 - 6*t + 1)

A162949 Number of reduced words of length n in Coxeter group on 8 generators S_i with relations (S_i)^2 = (S_i S_j)^4 = I.

Original entry on oeis.org

1, 8, 56, 392, 2716, 18816, 130368, 903168, 6257076, 43348536, 300314952, 2080556856, 14413923468, 99858452400, 691810982352, 4792808455344, 33204174947748, 230035738812264, 1593668302662744, 11040800320974312

Offset: 0

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

nonn

The initial terms coincide with those of A003950, 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 (6, 6, 6, -21).

coxG[{4,21,-6}] (* The coxG program is at A169452 *) (* Harvey P. Dale, May 04 2018 *)

G.f.: (t^4 + 2*t^3 + 2*t^2 + 2*t + 1)/(21*t^4 - 6*t^3 - 6*t^2 - 6*t + 1)

cp's OEIS Frontend

A168685 Number of reduced words of length n in Coxeter group on 8 generators S_i with relations (S_i)^2 = (S_i S_j)^17 = I.

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A168733 Number of reduced words of length n in Coxeter group on 8 generators S_i with relations (S_i)^2 = (S_i S_j)^18 = I.

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A168781 Number of reduced words of length n in Coxeter group on 8 generators S_i with relations (S_i)^2 = (S_i S_j)^19 = I.

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A168829 Number of reduced words of length n in Coxeter group on 8 generators S_i with relations (S_i)^2 = (S_i S_j)^20 = I.

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A169213 Number of reduced words of length n in Coxeter group on 8 generators S_i with relations (S_i)^2 = (S_i S_j)^28 = I.

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A169357 Number of reduced words of length n in Coxeter group on 8 generators S_i with relations (S_i)^2 = (S_i S_j)^31 = I.

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Mathematica

Formula

A169405 Number of reduced words of length n in Coxeter group on 8 generators S_i with relations (S_i)^2 = (S_i S_j)^32 = I.

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Mathematica

PARI

Formula

A170689 Number of reduced words of length n in Coxeter group on 8 generators S_i with relations (S_i)^2 = (S_i S_j)^50 = I.

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