A169452 -id:A169452 - cp's OEIS frontend

A163988 Number of reduced words of length n in Coxeter group on 22 generators S_i with relations (S_i)^2 = (S_i S_j)^6 = I.

1, 22, 462, 9702, 203742, 4278582, 89849991, 1886844960, 39623642520, 832094358480, 17473936704840, 366951729513600, 7705966552789890, 161824882502745000, 3398313815357307000, 71364407061765925800

Offset: 0

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

nonn

The initial terms coincide with those of A170741, 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..740
Index entries for linear recurrences with constant coefficients, signature (20, 20, 20, 20, 20, -210).

R:=PowerSeriesRing(Integers(), 20); Coefficients(R!( (1+x)*(1-x^6)/(1-21*x+230*x^6-210*x^7) )); // G. C. Greubel, Apr 25 2019

CoefficientList[Series[(1+x)*(1-x^6)/(1-21*x+230*x^6-210*x^7), {x,0,20}], x] (* G. C. Greubel, Aug 24 2017 *)
coxG[{6, 210, -20, 20}] (* The coxG program is at A169452 *)

my(x='x+O('x^20)); Vec((1+x)*(1-x^6)/(1-21*x+230*x^6-210*x^7)) \\ G. C. Greubel, Aug 24 2017, modified Apr 25 2019

((1+x)*(1-x^6)/(1-21*x+230*x^6-210*x^7)).series(x, 20).coefficients(x, sparse=False) # G. C. Greubel, Apr 25 2019

G.f.: (t^6 + 2*t^5 + 2*t^4 + 2*t^3 + 2*t^2 + 2*t + 1)/(210*t^6 - 20*t^5 - 20*t^4 - 20*t^3 - 20*t^2 - 20*t + 1).

G.f.: (1+x)*(1-x^6)/(1 -21*x +230*x^6 -210*x^7). - G. C. Greubel, Apr 25 2019

A163991 Number of reduced words of length n in Coxeter group on 23 generators S_i with relations (S_i)^2 = (S_i S_j)^6 = I.

Original entry on oeis.org

1, 23, 506, 11132, 244904, 5387888, 118533283, 2607726660, 57369864321, 1262134326684, 27766896042732, 610870411765152, 13439120433048156, 295660019761129485, 6504506579923898238, 143098839952914095019, 3148167773259336785958, 69259543486514630343864

Offset: 0

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

nonn

The initial terms coincide with those of A170742, 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..740
Index entries for linear recurrences with constant coefficients, signature (21,21,21,21,21,-231).

R:=PowerSeriesRing(Integers(), 20); Coefficients(R!( (1+x)*(1-x^6)/(1-22*x+252*x^6-231*x^7) )); // G. C. Greubel, Apr 25 2019

CoefficientList[Series[(1+x)*(1-x^6)/(1-22*x+252*x^6-231*x^7), {x,0,20}], x] (* G. C. Greubel, Aug 24 2017, modified Apr 25 2019 *)
coxG[{6, 231, -21}] (* The coxG program is at A169452 *) (* G. C. Greubel, Apr 25 2019 *)

my(x='x+O('x^20)); Vec((1+x)*(1-x^6)/(1-22*x+252*x^6-231*x^7)) \\ G. C. Greubel, Aug 24 2017, modified Apr 25 2019

((1+x)*(1-x^6)/(1-22*x+252*x^6-231*x^7)).series(x, 20).coefficients(x, sparse=False) # G. C. Greubel, Apr 25 2019

G.f.: (t^6 + 2*t^5 + 2*t^4 + 2*t^3 + 2*t^2 + 2*t + 1)/(231*t^6 - 21*t^5 - 21*t^4 - 21*t^3 - 21*t^2 - 21*t + 1).

G.f.: (1+x)*(1-x^6)/(1 -22*x +252*x^6 -231*x^7). - G. C. Greubel, Apr 25 2019

A164330 Number of reduced words of length n in Coxeter group on 45 generators S_i with relations (S_i)^2 = (S_i S_j)^6 = I.

Original entry on oeis.org

1, 45, 1980, 87120, 3833280, 168664320, 7421229090, 326534036400, 14367495685950, 632169725893200, 27815464230602400, 1223880262963776000, 53850724390367020710, 2369431557254469630780, 104254974618644628784170

Offset: 0

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

nonn

The initial terms coincide with those of A170764, 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..600
Index entries for linear recurrences with constant coefficients, signature (43, 43, 43, 43, 43, -946).

R:=PowerSeriesRing(Integers(), 20); Coefficients(R!( (1+x)*(1-x^6)/(1-44*x+989*x^6-946*x^7) )); // G. C. Greubel, Apr 25 2019

CoefficientList[Series[(1+x)*(1-x^6)/(1-44*x+989*x^6-946*x^7), {x,0,20}], x] (* G. C. Greubel, Sep 14 2017, modified Apr 25 2019 *)
coxG[{6, 946, -43}] (* The coxG program is at A169452 *) (* G. C. Greubel, Apr 25 2019 *)

my(x='x+O('x^20)); Vec((1+x)*(1-x^6)/(1-44*x+989*x^6-946*x^7)) \\ G. C. Greubel, Sep 14 2017, modified Apr 25 2019

((1+x)*(1-x^6)/(1-44*x+989*x^6-946*x^7)).series(x, 20).coefficients(x, sparse=False) # G. C. Greubel, Apr 25 2019

G.f.: (t^6 + 2*t^5 + 2*t^4 + 2*t^3 + 2*t^2 + 2*t + 1)/(946*t^6 - 43*t^5 - 43*t^4 - 43*t^3 - 43*t^2 - 43*t + 1).
G.f.: (1+x)*(1-x^6)/(1 -44*x +989*x^6 -946*x^7). - G. C. Greubel, Apr 25 2019
a(n) = -946*a(n-6) + 43*Sum_{k=1..5} a(n-k). - Wesley Ivan Hurt, May 06 2021

A164332 Number of reduced words of length n in Coxeter group on 47 generators S_i with relations (S_i)^2 = (S_i S_j)^6 = I.

Original entry on oeis.org

1, 47, 2162, 99452, 4574792, 210440432, 9680258791, 445291854660, 20483423028045, 942237354119580, 43342913451658140, 1993773796235517600, 91713584389960162440, 4218824411042032288125, 194065901246713684538250

Offset: 0

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

nonn

The initial terms coincide with those of A170766, 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..600
Index entries for linear recurrences with constant coefficients, signature (45, 45, 45, 45, 45, -1035).

R:=PowerSeriesRing(Integers(), 20); Coefficients(R!( (1+x)*(1-x^6)/(1-46*x+1080*x^6-1035*x^7) )); // G. C. Greubel, Apr 25 2019

CoefficientList[Series[(1+x)*(1-x^6)/(1-46*x+1080*x^6-1035*x^7), {x, 0, 20}], x] (* G. C. Greubel, Sep 14 2017, modified Apr 25 2019 *)
coxG[{6, 1035, -45}] (* The coxG program is at A169452 *) (* G. C. Greubel, Apr 25 2019 *)

my(x='x+O('x^20)); Vec((1+x)*(1-x^6)/(1-46*x+1080*x^6-1035*x^7)) \\ G. C. Greubel, Sep 14 2017, modified Apr 25 2019

((1+x)*(1-x^6)/(1-46*x+1080*x^6-1035*x^7)).series(x, 20).coefficients(x, sparse=False) # G. C. Greubel, Apr 25 2019

G.f.: (t^6 + 2*t^5 + 2*t^4 + 2*t^3 + 2*t^2 + 2*t + 1)/(1035*t^6 - 45*t^5 - 45*t^4 - 45*t^3 - 45*t^2 - 45*t + 1).
G.f.: (1+x)*(1-x^6)/(1 -46*x +1080*x^6 -1035*x^7). - G. C. Greubel, Apr 25 2019
a(n) = -1035*a(n-6) + 45*Sum_{k=1..5} a(n-k). - Wesley Ivan Hurt, May 06 2021

A164348 Number of reduced words of length n in Coxeter group on 48 generators S_i with relations (S_i)^2 = (S_i S_j)^6 = I.

Original entry on oeis.org

1, 48, 2256, 106032, 4983504, 234224688, 11008559208, 517402229760, 24317902308096, 1142941291421184, 53718235195007232, 2524756795581284352, 118663557238871024856, 5577186619014877732560, 262127744246735162576688

Offset: 0

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

nonn

The initial terms coincide with those of A170767, 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..595
Index entries for linear recurrences with constant coefficients, signature (46, 46, 46, 46, 46, -1081).

a:=[48, 2256, 106032, 4983504, 234224688, 11008559208];; for n in [7..20] do a[n]:=46*(a[n-1] +a[n-2]+a[n-3]+a[n-4]+a[n-5]) -1081*a[n-6]; od; Concatenation([1], a); # G. C. Greubel, Aug 24 2019

R:=PowerSeriesRing(Integers(), 20); Coefficients(R!( (1+t)*(1-t^6)/(1-47*t+1127*t^6-1081*t^7) )); // G. C. Greubel, Aug 24 2019

seq(coeff(series((1+t)*(1-t^6)/(1-47*t+1127*t^6-1081*t^7), t, n+1), t, n), n = 0..20); # G. C. Greubel, Aug 24 2019

CoefficientList[Series[(1+t)*(1-t^6)/(1-47*t+1127*t^6-1081*t^7), {t, 0, 20}], t] (* G. C. Greubel, Sep 15 2017 *)
coxG[{6, 1081, -46}] (* The coxG program is at A169452 *) (* G. C. Greubel, Aug 24 2019 *)

my(t='t+O('t^20)); Vec((1+t)*(1-t^6)/(1-47*t+1127*t^6-1081*t^7)) \\ G. C. Greubel, Sep 15 2017

def A164348_list(prec):
    P. = PowerSeriesRing(ZZ, prec)
    return P((1+t)*(1-t^6)/(1-47*t+1127*t^6-1081*t^7)).list()
A164348_list(20) # G. C. Greubel, Aug 24 2019

G.f.: (t^6 + 2*t^5 + 2*t^4 + 2*t^3 + 2*t^2 + 2*t + 1)/(1081*t^6 - 46*t^5 - 46*t^4 - 46*t^3 - 46*t^2 - 46*t + 1).

a(n) = -1081*a(n-6) + 46*Sum_{k=1..5} a(n-k). - Wesley Ivan Hurt, May 07 2021

A164369 Number of reduced words of length n in Coxeter group on 7 generators S_i with relations (S_i)^2 = (S_i S_j)^7 = I.

Original entry on oeis.org

1, 7, 42, 252, 1512, 9072, 54432, 326571, 1959300, 11755065, 70525980, 423129420, 2538617760, 15230754000, 91378809060, 548238566925, 3289225689750, 19734119944875, 118397314970550, 710339464409400, 4261770250642800

Offset: 0

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

nonn

The initial terms coincide with those of A003949, 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..1000
Index entries for linear recurrences with constant coefficients, signature (5, 5, 5, 5, 5, 5, -15).

R:=PowerSeriesRing(Integers(), 30); Coefficients(R!( (1+x)*(1-x^7)/(1-6*x+20*x^7-15*x^8) )); // G. C. Greubel, Apr 25 2019

CoefficientList[Series[(1+x)*(1-x^7)/(1-6*x+20*x^7-15*x^8), {x, 0, 30}], x] (* G. C. Greubel, Sep 17 2017, modified Apr 25 2019 *)
coxG[{7, 15, -5, 30}] (* The coxG program is at A169452 *) (* G. C. Greubel, Apr 25 2019 *)

my(x='x+O('x^30)); Vec((1+x)*(1-x^7)/(1-6*x+20*x^7-15*x^8)) \\ G. C. Greubel, Sep 17 2017, modified Apr 25 2019

((1+x)*(1-x^7)/(1-6*x+20*x^7-15*x^8)).series(x, 30).coefficients(x, sparse=False) # G. C. Greubel, Apr 25 2019

G.f.: (t^7 + 2*t^6 + 2*t^5 + 2*t^4 + 2*t^3 + 2*t^2 + 2*t + 1)/(15*t^7 - 5*t^6 - 5*t^5 - 5*t^4 - 5*t^3 - 5*t^2 - 5*t + 1).

G.f.: (1+x)*(1-x^7)/(1 -6*x +20*x^7 -15*x^8). - G. C. Greubel, Apr 25 2019

A164664 Number of reduced words of length n in Coxeter group on 28 generators S_i with relations (S_i)^2 = (S_i S_j)^7 = I.

Original entry on oeis.org

1, 28, 756, 20412, 551124, 14880348, 401769396, 10847773314, 292889869272, 7908026195160, 213516699839352, 5764950695053368, 155653663349994264, 4202648764205784984, 113471512684966713186, 3063730735882188973692

Offset: 0

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

nonn

The initial terms coincide with those of A170747, 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..695
Index entries for linear recurrences with constant coefficients, signature (26,26,26,26,26,26,-351).

Cf. A154638, A170747.

a:=[28,756,20412,551124,14880348,401769396,10847773314];; for n in [8..30] do a[n]:=26*(a[n-1] +a[n-2]+a[n-3]+a[n-4]+a[n-5]+a[n-6]) -351*a[n-7]; od; Concatenation([1], a); # G. C. Greubel, Sep 15 2019

R:=PowerSeriesRing(Integers(), 20); Coefficients(R!( (1+t)*(1-t^7)/(1-27*t+377*t^7-351*t^8) )); // G. C. Greubel, Sep 15 2019

seq(coeff(series((1+t)*(1-t^7)/(1-27*t+377*t^7-351*t^8), t, n+1), t, n), n = 0 .. 30); # G. C. Greubel, Sep 15 2019

CoefficientList[Series[(t^7 + 2*t^6 + 2*t^5 + 2*t^4 + 2*t^3 + 2*t^2 + 2*t + 1)/(351*t^7 - 26*t^6 - 26*t^5 - 26*t^4 - 26*t^3 - 26*t^2 - 26*t + 1), {t, 0, 20}], t] (* Wesley Ivan Hurt, Apr 25 2017 *)
coxG[{7,351,-26}] (* The coxG program is at A169452 *) (* Harvey P. Dale, Aug 13 2018 *)

my(t='t+O('t^20)); Vec((1+t)*(1-t^7)/(1-27*t+377*t^7-351*t^8)) \\ G. C. Greubel, Sep 15 2019

def A164664_list(prec):
    P. = PowerSeriesRing(ZZ, prec)
    return P((1+t)*(1-t^7)/(1-27*t+377*t^7-351*t^8)).list()
A164664_list(20) # G. C. Greubel, Sep 15 2019

G.f.: (t^7 + 2*t^6 + 2*t^5 + 2*t^4 + 2*t^3 + 2*t^2 + 2*t + 1)/(351*t^7 - 26*t^6 - 26*t^5 - 26*t^4 - 26*t^3 - 26*t^2 - 26*t + 1).

A164667 Number of reduced words of length n in Coxeter group on 31 generators S_i with relations (S_i)^2 = (S_i S_j)^7 = I.

Original entry on oeis.org

1, 31, 930, 27900, 837000, 25110000, 753300000, 22598999535, 677969972100, 20339098744965, 610172949807900, 18305188118005500, 549155632253220000, 16474668628988250000, 494240048711397215760, 14827201156594414216125

Offset: 0

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

nonn

The initial terms coincide with those of A170750, 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..670
Index entries for linear recurrences with constant coefficients, signature (29,29,29,29,29,29,-435).

a:=[31, 930, 27900, 837000, 25110000, 753300000, 22598999535];; for n in [8..20] do a[n]:=29*(a[n-1] +a[n-2]+a[n-3]+a[n-4]+a[n-5]+a[n-6]) -435*a[n-7]; od; Concatenation([1], a); # G. C. Greubel, Sep 15 2019

R:=PowerSeriesRing(Integers(), 20); Coefficients(R!( (1+t)*(1-t^7)/(1-30*t+464*t^7-435*t^8) )); // G. C. Greubel, Sep 15 2019

seq(coeff(series((1+t)*(1-t^7)/(1-30*t+464*t^7-435*t^8), t, n+1), t, n), n = 0 .. 20); # G. C. Greubel, Sep 15 2019

CoefficientList[Series[(1+t)*(1-t^7)/(1-30*t+464*t^7-435*t^8), {t, 0, 20}], t] (* G. C. Greubel, Sep 15 2019 *)
coxG[{7, 435, -29}] (* The coxG program is at A169452 *) (* G. C. Greubel, Sep 15 2019 *)

my(t='t+O('t^20)); Vec((1+t)*(1-t^7)/(1-30*t+464*t^7-435*t^8)) \\ G. C. Greubel, Sep 15 2019

def A164667_list(prec):
    P. = PowerSeriesRing(ZZ, prec)
    return P((1+t)*(1-t^7)/(1-30*t+464*t^7-435*t^8)).list()
A164667_list(20) # G. C. Greubel, Sep 15 2019

G.f.: (t^7 + 2*t^6 + 2*t^5 + 2*t^4 + 2*t^3 + 2*t^2 + 2*t + 1)/(435*t^7 - 29*t^6 - 29*t^5 - 29*t^4 - 29*t^3 - 29*t^2 - 29*t + 1).

A164670 Number of reduced words of length n in Coxeter group on 34 generators S_i with relations (S_i)^2 = (S_i S_j)^7 = I.

Original entry on oeis.org

1, 34, 1122, 37026, 1221858, 40321314, 1330603362, 43909910385, 1449027024192, 47817891187968, 1577990389060800, 52073682174315648, 1718431489817621568, 56708238440133282816, 1871371844637407092464, 61755270084763733187072

Offset: 0

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

nonn

The initial terms coincide with those of A170753, 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..655
Index entries for linear recurrences with constant coefficients, signature (32,32,32,32,32,32,-528).

a:=[34, 1122, 37026, 1221858, 40321314, 1330603362, 43909910385];; for n in [8..20] do a[n]:=32*(a[n-1] +a[n-2]+a[n-3]+a[n-4]+a[n-5]+a[n-6]) -528*a[n-7]; od; Concatenation([1], a); # G. C. Greubel, Sep 15 2019

R:=PowerSeriesRing(Integers(), 20); Coefficients(R!( (1+t)*(1-t^7)/(1-33*t+560*t^7-528*t^8) )); // G. C. Greubel, Sep 15 2019

seq(coeff(series((1+t)*(1-t^7)/(1-33*t+560*t^7-528*t^8), t, n+1), t, n), n = 0 .. 20); # G. C. Greubel, Sep 15 2019

CoefficientList[Series[(1+t)*(1-t^7)/(1-33*t+560*t^7-528*t^8), {t, 0, 20}], t] (* G. C. Greubel, Sep 15 2019 *)
coxG[{7, 528, -32}] (* The coxG program is at A169452 *) (* G. C. Greubel, Sep 15 2019 *)

my(t='t+O('t^20)); Vec((1+t)*(1-t^7)/(1-33*t+560*t^7-528*t^8)) \\ G. C. Greubel, Sep 15 2019

def A164670_list(prec):
    P. = PowerSeriesRing(ZZ, prec)
    return P((1+t)*(1-t^7)/(1-33*t+560*t^7-528*t^8)).list()
A164670_list(20) # G. C. Greubel, Sep 15 2019

G.f.: (t^7 + 2*t^6 + 2*t^5 + 2*t^4 + 2*t^3 + 2*t^2 + 2*t + 1)/(528*t^7 - 32*t^6 - 32*t^5 - 32*t^4 - 32*t^3 - 32*t^2 - 32*t + 1).

A164681 Number of reduced words of length n in Coxeter group on 39 generators S_i with relations (S_i)^2 = (S_i S_j)^7 = I.

Original entry on oeis.org

1, 39, 1482, 56316, 2140008, 81320304, 3090171552, 117426518235, 4462207664772, 169563890192073, 6443427786666780, 244850254349321868, 9304309606601631648, 353563762821303227856, 13435422902486289765684

Offset: 0

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

The initial terms coincide with those of A170758, although the two sequences are eventually different.

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 (37, 37, 37, 37, 37, 37, -703).

R:=PowerSeriesRing(Integers(), 20); Coefficients(R!( (1+x)*(1-x^7)/(1 -38*x +740*x^7 -703*x^8) )); // G. C. Greubel, Apr 26 2019

CoefficientList[Series[(x^7 + 2 x^6 + 2 x^5 + 2 x^4 + 2 x^3 + 2 x^2 + 2 x + 1)/(703 x^7 - 37 x^6 - 37 x^5 - 37 x^4 - 37 x^3 - 37 x^2 - 37 x + 1), {x, 0, 20}], x ] (* Vincenzo Librandi, Apr 29 2014 *)
coxG[{7, 703, -37}] (* The coxG program is at A169452 *) (* G. C. Greubel, Apr 26 2019 *)

my(x='x+O('x^20)); Vec((1+x)*(1-x^7)/(1-38*x+740*x^7-703*x^8)) \\ G. C. Greubel, Apr 26 2019

((1+x)*(1-x^7)/(1 -38*x +740*x^7 -703*x^8)).series(x, 20).coefficients(x, sparse=False) # G. C. Greubel, Apr 26 2019

G.f.: (x^7 + 2*x^6 + 2*x^5 + 2*x^4 + 2*x^3 + 2*x^2 + 2*x + 1)/(703*x^7 - 37*x^6 - 37*x^5 - 37*x^4 - 37*x^3 - 37*x^2 - 37*x + 1).

G.f.: (1+x)*(1-x^7)/(1 -38*x +740*x^7 -703*x^8). - G. C. Greubel, Apr 26 2019

cp's OEIS Frontend

A163988 Number of reduced words of length n in Coxeter group on 22 generators S_i with relations (S_i)^2 = (S_i S_j)^6 = I.

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A163991 Number of reduced words of length n in Coxeter group on 23 generators S_i with relations (S_i)^2 = (S_i S_j)^6 = I.

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A164330 Number of reduced words of length n in Coxeter group on 45 generators S_i with relations (S_i)^2 = (S_i S_j)^6 = I.

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A164332 Number of reduced words of length n in Coxeter group on 47 generators S_i with relations (S_i)^2 = (S_i S_j)^6 = I.

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A164348 Number of reduced words of length n in Coxeter group on 48 generators S_i with relations (S_i)^2 = (S_i S_j)^6 = I.

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A164369 Number of reduced words of length n in Coxeter group on 7 generators S_i with relations (S_i)^2 = (S_i S_j)^7 = I.

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Magma

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PARI

Sage

Formula

A164664 Number of reduced words of length n in Coxeter group on 28 generators S_i with relations (S_i)^2 = (S_i S_j)^7 = I.

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