A003952 -id:A003952 - cp's OEIS frontend

A164779 Number of reduced words of length n in Coxeter group on 10 generators S_i with relations (S_i)^2 = (S_i S_j)^8 = I.

1, 10, 90, 810, 7290, 65610, 590490, 5314410, 47829645, 430466400, 3874194000, 34867713600, 313809130800, 2824279552800, 25418492355600, 228766218624000, 2058894054430380, 18530029271219040, 166770108473225760

Offset: 0

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

nonn

The initial terms coincide with those of A003952, 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 (8, 8, 8, 8, 8, 8, 8, -36).

R:=PowerSeriesRing(Integers(), 20); Coefficients(R!( (1+x)*(1-x^8)/(1-9*x+44*x^8-36*x^9) )); // G. C. Greubel, Apr 26 2019

coxG[{8,36,-8}] (* The coxG program is at A169452 *) (* Harvey P. Dale, Jun 13 2017 *)
CoefficientList[Series[(1+x)*(1-x^8)/(1-9*x+44*x^8-36*x^9), {x,0,20}], x] (* G. C. Greubel, Apr 26 2019 *)

my(x='x+O('x^20)); Vec((1+x)*(1-x^8)/(1-9*x+44*x^8-36*x^9)) \\ G. C. Greubel, Apr 26 2019

((1+x)*(1-x^8)/(1-9*x+44*x^8-36*x^9)).series(x, 20).coefficients(x, sparse=False) # G. C. Greubel, Apr 26 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)/( 36*t^8 - 8*t^7 - 8*t^6 - 8*t^5 - 8*t^4 - 8*t^3 - 8*t^2 - 8*t + 1).

G.f.: (1+x)*(1-x^8)/(1 -9*x +44*x^8 -36*x^9). - G. C. Greubel, Apr 26 2019

A162983 Number of reduced words of length n in Coxeter group on 10 generators S_i with relations (S_i)^2 = (S_i S_j)^4 = I.

Original entry on oeis.org

1, 10, 90, 810, 7245, 64800, 579600, 5184000, 46366380, 414707040, 3709193760, 33175513440, 296726124240, 2653957198080, 23737339710720, 212309865780480, 1898927161041600, 16984252473131520, 151909371770042880

Offset: 0

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

nonn

The initial terms coincide with those of A003952, 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 (8, 8, 8, -36).

a:=[10,90,810,7245];; for n in [5..20] do a[n]:=8*(a[n-1]+a[n-2] +a[n-3]) - 36*a[n-4]; od; Concatenation([1], a); # G. C. Greubel, Apr 28 2019

R:=PowerSeriesRing(Integers(), 20); Coefficients(R!( (1+x)*(1-x^4)/(1-9*x+44*x^4-36*x^5) )); // G. C. Greubel, Apr 28 2019

CoefficientList[Series[(1+x)*(1-x^4)/(1-9*x+44*x^4-36*x^5), {x,0,20}], x]
(* or *) coxG[{4, 36, -8}] (* The coxG program is at A169452 *) (* G. C. Greubel, Apr 28 2019 *)

my(x='x+O('x^20)); Vec((1+x)*(1-x^4)/(1-9*x+44*x^4-36*x^5)) \\ G. C. Greubel, Apr 28 2019

((1+x)*(1-x^4)/(1-9*x+44*x^4-36*x^5)).series(x, 20).coefficients(x, sparse=False) # G. C. Greubel, Apr 28 2019

G.f.: (t^4 + 2*t^3 + 2*t^2 + 2*t + 1)/(36*t^4 - 8*t^3 - 8*t^2 - 8*t + 1).
From G. C. Greubel, Apr 28 2019: (Start)
a(n) = 8*(a(n-1) + a(n-2) + a(n-3)) - 36*a(n-4).
G.f.: (1+x)*(1-x^4)/(1 - 9*x + 44*x^4 - 36*x^5). (End)

A163397 Number of reduced words of length n in Coxeter group on 10 generators S_i with relations (S_i)^2 = (S_i S_j)^5 = I.

Original entry on oeis.org

1, 10, 90, 810, 7290, 65565, 589680, 5303520, 47699280, 429001920, 3858394860, 34701968160, 312105587040, 2807042441760, 25246223065440, 227061682284240, 2042167156174080, 18367021030590720, 165190915209012480

Offset: 0

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

nonn

The initial terms coincide with those of A003952, 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 (8, 8, 8, 8, -36).

R:=PowerSeriesRing(Integers(), 30); Coefficients(R!( (1+x)*(1-x^5)/(1-9*x+44*x^5-36*x^6) )); // G. C. Greubel, May 12 2019

CoefficientList[Series[(1+x)*(1-x^5)/(1-9*x+44*x^5-36*x^6), {x, 0, 30}], x] (* or *) LinearRecurrence[{8,8,8,8,-36}, {1,10,90,810,7290,65565}, 30] (* G. C. Greubel, Dec 21 2016 *)
coxG[{5, 36, -8}] (* The coxG program is at A169452 *) (* G. C. Greubel, May 12 2019 *)

my(x='x+O('x^30)); Vec((1+x)*(1-x^5)/(1-9*x+44*x^5-36*x^6)) \\ G. C. Greubel, Dec 21 2016

((1+x)*(1-x^5)/(1-9*x+44*x^5-36*x^6)).series(x, 30).coefficients(x, sparse=False) # G. C. Greubel, May 12 2019

G.f.: (t^5 + 2*t^4 + 2*t^3 + 2*t^2 + 2*t + 1)/(36*t^5 - 8*t^4 - 8*t^3 - 8*t^2 - 8*t + 1).

a(n) = 8*a(n-1)+8*a(n-2)+8*a(n-3)+8*a(n-4)-36*a(n-5). - Wesley Ivan Hurt, May 10 2021

A163954 Number of reduced words of length n in Coxeter group on 10 generators S_i with relations (S_i)^2 = (S_i S_j)^6 = I.

Original entry on oeis.org

1, 10, 90, 810, 7290, 65610, 590445, 5313600, 47818800, 430336800, 3872739600, 34852032000, 313644670380, 2822589491040, 25401392681760, 228595320793440, 2057202978723360, 18513432737727840, 166608348947205840

Offset: 0

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

nonn

The initial terms coincide with those of A003952, 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 (8,8,8,8,8,-36).

a:=[10, 90, 810, 7290, 65610, 590445];; for n in [7..30] do a[n]:=8*(a[n-1]+a[n-2]+a[n-3]+a[n-4]+a[n-5]) -36*a[n-6]; od; Concatenation([1], a); # G. C. Greubel, Aug 10 2019

R:=PowerSeriesRing(Integers(), 30); Coefficients(R!( (1+t)*(1-t^6)/(1-9*t+44*t^6-36*t^7) )); // G. C. Greubel, Aug 10 2019

seq(coeff(series((1+t)*(1-t^6)/(1-9*t+44*t^6-36*t^7), t, n+1), t, n), n = 0 .. 30); # G. C. Greubel, Aug 10 2019

CoefficientList[Series[(1+t)*(1-t^6)/(1-9*t+44*t^6-36*t^7), {t, 0, 30}], t] (* G. C. Greubel, Aug 13 2017 *)
coxG[{6, 36, -8}] (* The coxG program is at A169452 *) (* G. C. Greubel, Aug 10 2019 *)

my(t='t+O('t^30)); Vec((1+t)*(1-t^6)/(1-9*t+44*t^6-36*t^7)) \\ G. C. Greubel, Aug 13 2017

def A163954_list(prec):
    P. = PowerSeriesRing(ZZ, prec)
    return P((1+t)*(1-t^6)/(1-9*t+44*t^6-36*t^7)).list()
A163954_list(30) # G. C. Greubel, Aug 10 2019

G.f.: (t^6 + 2*t^5 + 2*t^4 + 2*t^3 + 2*t^2 + 2*t + 1)/(36*t^6 - 8*t^5 - 8*t^4 - 8*t^3 - 8*t^2 - 8*t + 1).

a(n) = -36*a(n-6) + 8*Sum_{k=1..5} a(n-k). - Wesley Ivan Hurt, May 11 2021

A164548 Number of reduced words of length n in Coxeter group on 10 generators S_i with relations (S_i)^2 = (S_i S_j)^7 = I.

Original entry on oeis.org

1, 10, 90, 810, 7290, 65610, 590490, 5314365, 47828880, 430456320, 3874074480, 34866378720, 313794784080, 2824129437120, 25416952359660, 228750658083360, 2058738704511840, 18528493377756960, 166755045745830240

Offset: 0

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

nonn

The initial terms coincide with those of A003952, 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 (8,8,8,8,8,8,-36).

R:=PowerSeriesRing(Integers(), 30);
Coefficients(R!( (1+t)*(1-t^7)/(1 -9*t +44*t^7 -36*t^8) )); // G. C. Greubel, Jul 17 2021

CoefficientList[Series[(1+t)*(1-t^7)/(1 -9*t +44*t^7 -36*t^8), {t,0,30}], t] (* or *)
coxG[{7, 36, -8, 30}] (* The coxG program is at A169452 *) (* G. C. Greubel, Jul 17 2021 *)

def A168823_list(prec):
    P. = PowerSeriesRing(ZZ, prec)
    return P( (1+t)*(1-t^7)/(1 -9*t +44*t^7 -36*t^8) ).list()
A168823_list(30) # G. C. Greubel, Jul 17 2021

G.f.: (t^7 + 2*t^6 + 2*t^5 + 2*t^4 + 2*t^3 + 2*t^2 + 2*t + 1)/(36*t^7 - 8*t^6 - 8*t^5 - 8*t^4 - 8*t^3 - 8*t^2 - 8*t + 1).

G.f.: (1+t)*(1-t^7)/(1 -9*t +44*t^7 -36*t^8). - G. C. Greubel, Jul 17 2021

A165788 Number of reduced words of length n in Coxeter group on 10 generators S_i with relations (S_i)^2 = (S_i S_j)^10 = I.

Original entry on oeis.org

1, 10, 90, 810, 7290, 65610, 590490, 5314410, 47829690, 430467210, 3874204845, 34867843200, 313810585200, 2824295234400, 25418656818000, 228767908737600, 2058911155018800, 18530200182592800, 166771799730147600

Offset: 0

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

nonn

The initial terms coincide with those of A003952, 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 (8,8,8,8,8,8,8,8,8,-36).

a:=[10, 90, 810, 7290, 65610, 590490, 5314410, 47829690, 430467210, 3874204845];; for n in [11..20] do a[n]:=8*Sum([1..9], j-> a[n-j]) -36*a[n-10]; od; Concatenation([1], a); # G. C. Greubel, Sep 22 2019

R:=PowerSeriesRing(Integers(), 20); Coefficients(R!( (1+t)*(1-t^10)/(1-9*t+44*t^10-36*t^11) )); // G. C. Greubel, Sep 22 2019

seq(coeff(series((1+t)*(1-t^10)/(1-9*t+44*t^10-36*t^11), t, n+1), t, n), n = 0..20); # G. C. Greubel, Aug 10 2019

CoefficientList[Series[(1+t)*(1-t^10)/(1-9*t+44*t^10-36*t^11), {t, 0, 25}], t] (* G. C. Greubel, Apr 08 2016 *)
coxG[{10, 36, -8}] (* The coxG program is at A169452 *) (* G. C. Greubel, Sep 22 2019 *)

my(t='t+O('t^20)); Vec((1+t)*(1-t^10)/(1-9*t+44*t^10-36*t^11)) \\ G. C. Greubel, Sep 22 2019

def A165788_list(prec):
    P. = PowerSeriesRing(ZZ, prec)
    return P((1+t)*(1-t^10)/(1-9*t+44*t^10-36*t^11)).list()
A165788_list(20) # G. C. Greubel, Sep 22 2019

G.f.: (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)/(36*t^10 - 8*t^9 - 8*t^8 - 8*t^7 - 8*t^6 - 8*t^5 - 8*t^4 - 8*t^3 - 8*t^2 - 8*t + 1).

A166368 Number of reduced words of length n in Coxeter group on 10 generators S_i with relations (S_i)^2 = (S_i S_j)^11 = I.

Original entry on oeis.org

1, 10, 90, 810, 7290, 65610, 590490, 5314410, 47829690, 430467210, 3874204890, 34867843965, 313810595280, 2824295353920, 25418658152880, 228767923084320, 2058911305134480, 18530201722590720, 166771815290740080

Offset: 0

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

nonn

The initial terms coincide with those of A003952, 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 (8,8,8,8,8,8,8,8,8,8,-36).

Cf. A003952, A154638, A169452.

R:=PowerSeriesRing(Integers(), 30);
Coefficients(R!( (1+x)*(1-x^11)/(1-9*x+44*x^16-36*x^17) )); // G. C. Greubel, Jul 23 2024

seq(coeff(series((1+t)*(1-t^11)/(1-9*t+44*t^11-36*t^12), t, n+1), t, n), n = 0 .. 30); # G. C. Greubel, Mar 14 2020

CoefficientList[Series[(1+t)*(1-t^11)/(1-9*t+44*t^11-36*t^12), {t,0,30}], t] (* G. C. Greubel, May 10 2016 *)
coxG[{11, 36, -8}] (* The coxG program is in A169452 *) (* G. C. Greubel, Mar 14 2020 *)

def A166368_list(prec):
    P. = PowerSeriesRing(ZZ, prec)
    return P( (1+t)*(1-t^11)/(1-9*t+44*t^11-36*t^12) ).list()
A166368_list(30) # G. C. Greubel, Mar 14 2020

G.f.: (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)/(36*t^11 - 8*t^10 - 8*t^9 - 8*t^8 - 8*t^7 - 8*t^6 - 8*t^5 - 8*t^4 - 8*t^3 - 8*t^2 - 8*t + 1).
From G. C. Greubel, Jul 23 2024: (Start)
a(n) = 8*Sum_{j=1..10} a(n-j) - 36*a(n-11).
G.f.: (1+t)*(1 - t^11)/(1 - 9*t + 44*t^11 - 36*t^12). (End)

A166543 Number of reduced words of length n in Coxeter group on 10 generators S_i with relations (S_i)^2 = (S_i S_j)^12 = I.

Original entry on oeis.org

1, 10, 90, 810, 7290, 65610, 590490, 5314410, 47829690, 430467210, 3874204890, 34867844010, 313810596045, 2824295364000, 25418658272400, 228767924419200, 2058911319481200, 18530201872706400, 166771816830738000

Offset: 0

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

nonn

The initial terms coincide with those of A003952, 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 (8,8,8,8,8,8,8,8,8,8,8,-36).

Cf. A003952, A154638, A169452.

R:=PowerSeriesRing(Integers(), 30); Coefficients(R!( (1+x)*(1-x^12)/(1-9*x+44*x^12-36*x^13) )); // G. C. Greubel, Aug 23 2024

CoefficientList[Series[(1+t)*(1-t^12)/(1-9*t+44*t^12-36*t^13), {t, 0, 50}], t] (* G. C. Greubel, May 16 2016; Aug 23 2024 *)
coxG[{12,36,-8,30}] (* The coxG program is at A169452 *) (* G. C. Greubel, Aug 23 2024 *)

def A166543_list(prec):
    P. = PowerSeriesRing(ZZ, prec)
    return P( (1+x)*(1-x^12)/(1-9*x+44*x^12-36*x^13) ).list()
A166543_list(30) # G. C. Greubel, Aug 23 2024

G.f.: (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)/(36*t^12 - 8*t^11 - 8*t^10 - 8*t^9 - 8*t^8 - 8*t^7 - 8*t^6 - 8*t^5 - 8*t^4 - 8*t^3 - 8*t^2 - 8*t + 1).
From G. C. Greubel, Aug 23 2024: (Start)
a(n) = 8*Sum_{j=1..11} a(n-j) - 36*a(n-12).
G.f.: (1+x)*(1-x^12)/(1 - 9*x + 44*x^12 - 36*x^13). (End)

A166933 Number of reduced words of length n in Coxeter group on 10 generators S_i with relations (S_i)^2 = (S_i S_j)^13 = I.

Original entry on oeis.org

1, 10, 90, 810, 7290, 65610, 590490, 5314410, 47829690, 430467210, 3874204890, 34867844010, 313810596090, 2824295364765, 25418658282480, 228767924538720, 2058911320816080, 18530201887053120, 166771816980853680

Offset: 0

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

nonn

The initial terms coincide with those of A003952, 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 (8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, -36).

CoefficientList[Series[(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)/(36*t^13 - 8*t^12 - 8*t^11 - 8*t^10 - 8*t^9 - 8*t^8 - 8*t^7 - 8*t^6 - 8*t^5 - 8*t^4 - 8*t^3 - 8*t^2 - 8*t + 1), {t, 0, 50}], t] (* G. C. Greubel, May 28 2016 *)

G.f.: (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)/(36*t^13 - 8*t^12 - 8*t^11 - 8*t^10 - 8*t^9 - 8*t^8 - 8*t^7 - 8*t^6 - 8*t^5 - 8*t^4 - 8*t^3 - 8*t^2 - 8*t + 1).

A167111 Number of reduced words of length n in Coxeter group on 10 generators S_i with relations (S_i)^2 = (S_i S_j)^14 = I.

Original entry on oeis.org

1, 10, 90, 810, 7290, 65610, 590490, 5314410, 47829690, 430467210, 3874204890, 34867844010, 313810596090, 2824295364810, 25418658283245, 228767924548800, 2058911320935600, 18530201888388000, 166771816995200400

Offset: 0

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

nonn

The initial terms coincide with those of A003952, 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 (8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, -36).

CoefficientList[Series[(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)/ (36*t^14 - 8*t^13 - 8*t^12 - 8*t^11 - 8*t^10 - 8*t^9 - 8*t^8 - 8*t^7 - 8*t^6 - 8*t^5 - 8*t^4 - 8*t^3 - 8*t^2 - 8*t + 1), {t, 0, 50}], t] (* G. C. Greubel, Jun 03 2016 *)

G.f.: (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)/(36*t^14 - 8*t^13 - 8*t^12 - 8*t^11 - 8*t^10 - 8*t^9 - 8*t^8 - 8*t^7 - 8*t^6 - 8*t^5 - 8*t^4 - 8*t^3 - 8*t^2 - 8*t + 1).

cp's OEIS Frontend

A164779 Number of reduced words of length n in Coxeter group on 10 generators S_i with relations (S_i)^2 = (S_i S_j)^8 = I.

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A162983 Number of reduced words of length n in Coxeter group on 10 generators S_i with relations (S_i)^2 = (S_i S_j)^4 = I.

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A163397 Number of reduced words of length n in Coxeter group on 10 generators S_i with relations (S_i)^2 = (S_i S_j)^5 = I.

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A163954 Number of reduced words of length n in Coxeter group on 10 generators S_i with relations (S_i)^2 = (S_i S_j)^6 = I.

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A164548 Number of reduced words of length n in Coxeter group on 10 generators S_i with relations (S_i)^2 = (S_i S_j)^7 = I.

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A165788 Number of reduced words of length n in Coxeter group on 10 generators S_i with relations (S_i)^2 = (S_i S_j)^10 = I.

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A166368 Number of reduced words of length n in Coxeter group on 10 generators S_i with relations (S_i)^2 = (S_i S_j)^11 = I.

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