cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

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A163223 Number of reduced words of length n in Coxeter group on 40 generators S_i with relations (S_i)^2 = (S_i S_j)^4 = I.

Original entry on oeis.org

1, 40, 1560, 60840, 2371980, 92476800, 3605409600, 140564736000, 5480222014020, 213658376756760, 8329936604744040, 324760699264187160, 12661502336823753660, 493636212105145265520, 19245481572342746507280
Offset: 0

Views

Author

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

Keywords

Comments

The initial terms coincide with those of A170759, although the two sequences are eventually different.
Computed with MAGMA using commands similar to those used to compute A154638.

Links

Crossrefs

Cf. A154638, A170759.

Programs

  • Magma
    R:=PowerSeriesRing(Integers(), 20); Coefficients(R!( (1+x)*(1-x^4)/(1-39*x+779*x^4-741*x^5) )); // G. C. Greubel, Apr 30 2019
  • Mathematica
    CoefficientList[Series[(t^4+2*t^3+2*t^2+2*t+1)/(741*t^4-38*t^3-38*t^2 - 38*t+1), {t, 0, 20}], t] (* or *) LinearRecurrence[{38, 38, 38, -741}, {1, 40, 1560, 60840, 2371980}, 20] (* G. C. Greubel, Dec 11 2016 *)
coxG[{4, 741, -38}] (* The coxG program is at A169452 *) (* G. C. Greubel, Apr 30 2019 *)
  • PARI
    my(t='t+O('t^20)); Vec((t^4+2*t^3+2*t^2+2*t+1)/(741*t^4- 38*t^3 -38*t^2-38*t+1)) \\ G. C. Greubel, Dec 11 2016
  • Sage
    ((1+x)*(1-x^4)/(1-39*x+779*x^4-741*x^5)).series(x, 20).coefficients(x, sparse=False) # G. C. Greubel, Apr 30 2019

Formula

G.f.: (t^4 + 2*t^3 + 2*t^2 + 2*t + 1)/(741*t^4 - 38*t^3 - 38*t^2 - 38*t + 1).
a(n) = 38*a(n-1)+38*a(n-2)+38*a(n-3)-741*a(n-4). - Wesley Ivan Hurt, May 06 2021

A163224 Number of reduced words of length n in Coxeter group on 41 generators S_i with relations (S_i)^2 = (S_i S_j)^4 = I.

Original entry on oeis.org

1, 41, 1640, 65600, 2623180, 104894400, 4194464820, 167726145600, 6706948607580, 268194081870000, 10724409825744420, 428842296999090000, 17148329715447559980, 685718769084764781600, 27420176663127165184020
Offset: 0

Views

Author

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

Keywords

Comments

The initial terms coincide with those of A170760, although the two sequences are eventually different.
Computed with MAGMA using commands similar to those used to compute A154638.

Links

Programs

  • Magma
    R:=PowerSeriesRing(Integers(), 20); Coefficients(R!( (1+x)*(1-x^4)/(1-40*x+819*x^4-780*x^5) )); // G. C. Greubel, Apr 30 2019
  • Mathematica
    CoefficientList[Series[(t^4+2*t^3+2*t^2+2*t+1)/(780*t^4-39*t^3-39*t^2 - 39*t+1), {t,0,20}], t] (* or *) Join[{1}, LinearRecurrence[ {39, 39, 39, -780}, {41,1640,65600,2623180} 20]] (* G. C. Greubel, Dec 11 2016 *)
coxG[{4,780,-39}] (* The coxG program is at A169452 *) (* Harvey P. Dale, Jan 18 2019 *)
  • PARI
    my(t='t+O('t^20)); Vec((t^4+2*t^3+2*t^2+2*t+1)/(780*t^4-39*t^3- 39*t^2-39*t+1)) \\ G. C. Greubel, Dec 11 2016
  • Sage
    ((1+x)*(1-x^4)/(1-40*x+819*x^4-780*x^5)).series(x, 20).coefficients(x, sparse=False) # G. C. Greubel, Apr 30 2019

Formula

G.f.: (t^4 + 2*t^3 + 2*t^2 + 2*t + 1)/(780*t^4 - 39*t^3 - 39*t^2 - 39*t + 1).
a(n) = 39*a(n-1)+39*a(n-2)+39*a(n-3)-780*a(n-4). - Wesley Ivan Hurt, May 06 2021

A163226 Number of reduced words of length n in Coxeter group on 43 generators S_i with relations (S_i)^2 = (S_i S_j)^4 = I.

Original entry on oeis.org

1, 43, 1806, 75852, 3184881, 133727076, 5614945203, 235760834988, 9899147615406, 415646320207041, 17452195907135052, 732784406294332791, 30768219023291805678, 1291898809163525952060, 54244365975641552431917
Offset: 0

Views

Author

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

Keywords

Comments

The initial terms coincide with those of A170762, although the two sequences are eventually different.
Computed with MAGMA using commands similar to those used to compute A154638.

Links

Programs

  • Magma
    R:=PowerSeriesRing(Integers(), 20); Coefficients(R!( (1+x)*(1-x^4)/(1-42*x+902*x^4-861*x^5) )); // G. C. Greubel, Apr 30 2019
  • Mathematica
    CoefficientList[Series[(t^4+2*t^3+2*t^2+2*t+1)/(861*t^4-41*t^3-41*t^2 - 41*t+1), {t,0,20}], t] (* or *) Join[{1}, LinearRecurrence[ {41, 41, 41, -861}, {43,1806,75852,3184881}, 20]] (* G. C. Greubel, Dec 11 2016 *)
coxG[{4, *61, -41}] (* The coxG program is at A169452 *) (* G. C. Greubel, Apr 30 2019 *)
  • PARI
    my(t='t+O('t^20)); Vec((t^4+2*t^3+2*t^2+2*t+1)/(861*t^4-41*t^3 - 41*t^2-41*t+1)) \\ G. C. Greubel, Dec 11 2016
  • Sage
    ((1+x)*(1-x^4)/(1-42*x+902*x^4-861*x^5)).series(x, 20).coefficients(x, sparse=False) # G. C. Greubel, Apr 30 2019

Formula

G.f.: (t^4 + 2*t^3 + 2*t^2 + 2*t + 1)/(861*t^4 - 41*t^3 - 41*t^2 - 41*t + 1).
a(n) = 41*a(n-1)+41*a(n-2)+41*a(n-3)-861*a(n-4). - Wesley Ivan Hurt, May 06 2021

A163230 Number of reduced words of length n in Coxeter group on 44 generators S_i with relations (S_i)^2 = (S_i S_j)^4 = I.

Original entry on oeis.org

1, 44, 1892, 81356, 3497362, 150345888, 6463124976, 277839201024, 11943854101410, 513446807614356, 22072240836651852, 948849634132915284, 40789498214388049434, 1753474001285744132472, 75378987430163637459624
Offset: 0

Views

Author

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

Keywords

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

Programs

  • Magma
    R:=PowerSeriesRing(Integers(), 20); Coefficients(R!( (1+x)*(1-x^4)/(1-43*x+945*x^4-903*x^5) )); // G. C. Greubel, Apr 30 2019
  • Mathematica
    coxG[{4,903,-42}] (* The coxG program is at A169452 *) (* Harvey P. Dale, Apr 18 2015 *)
CoefficientList[Series[(t^4+2*t^3+2*t^2+2*t+1)/(903*t^4-42*t^3-42*t^2 - 42*t+1), {t,0,20}], t] (* or *) Join[{1}, LinearRecurrence[ {42, 42, 42, -903}, {44,1892,81356,3497362}, 50]] (* G. C. Greubel, Dec 11 2016 *)
  • PARI
    my(t='t+O('t^20)); Vec((t^4+2*t^3+2*t^2+2*t+1)/(903*t^4-42*t^3 - 42*t^2-42*t+1)) \\ G. C. Greubel, Dec 11 2016
  • Sage
    ((1+x)*(1-x^4)/(1-43*x+945*x^4-903*x^5)).series(x, 20).coefficients(x, sparse=False) # G. C. Greubel, Apr 30 2019

Formula

G.f.: (t^4 + 2*t^3 + 2*t^2 + 2*t + 1)/(903*t^4 - 42*t^3 - 42*t^2 - 42*t + 1).
a(n) = 42*a(n-1)+42*a(n-2)+42*a(n-3)-903*a(n-4). - Wesley Ivan Hurt, May 06 2021

A163231 Number of reduced words of length n in Coxeter group on 45 generators S_i with relations (S_i)^2 = (S_i S_j)^4 = I.

Original entry on oeis.org

1, 45, 1980, 87120, 3832290, 168577200, 7415481150, 326196882000, 14348955088710, 631190926398780, 27765226324720170, 1221354364616557380, 53725709508796162530, 2363320544672336677560, 103959241263364038810390
Offset: 0

Views

Author

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

Keywords

Comments

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.

Links

Programs

  • Magma
    R:=PowerSeriesRing(Integers(), 30); Coefficients(R!( (1+x)*(1-x^4)/(1-44*x+989*x^4-946*x^5) )); // G. C. Greubel, Apr 30 2019
  • Mathematica
    CoefficientList[Series[(t^4+2*t^3+2*t^2+2*t+1)/(946*t^4-43*t^3-43*t^2 - 43*t+1), {t,0,20}], t] (* or *) Join[{1}, LinearRecurrence[ {43, 43, 43, -946}, {45,1980,87120,3832290}, 20]] (* G. C. Greubel, Dec 11 2016 *)
coxG[{4, 946, -43}] (* The coxG program is at A169452 *) (* G. C. Greubel, Apr 30 2019 *)
  • PARI
    my(t='t+O('t^20)); Vec((t^4+2*t^3+2*t^2+2*t+1)/(946*t^4-43*t^3 - 43*t^2-43*t+1)) \\ G. C. Greubel, Dec 11 2016
  • Sage
    ((1+x)*(1-x^4)/(1-44*x+989*x^4-946*x^5)).series(x, 30).coefficients(x, sparse=False) # G. C. Greubel, Apr 30 2019

Formula

G.f.: (t^4 + 2*t^3 + 2*t^2 + 2*t + 1)/(946*t^4 - 43*t^3 - 43*t^2 - 43*t + 1).
a(n) = 43*a(n-1)+43*a(n-2)+43*a(n-3)-946*a(n-4). - Wesley Ivan Hurt, May 06 2021

A163232 Number of reduced words of length n in Coxeter group on 46 generators S_i with relations (S_i)^2 = (S_i S_j)^4 = I.

Original entry on oeis.org

1, 46, 2070, 93150, 4190715, 188535600, 8482007160, 381596054400, 17167581467190, 772350369021000, 34747182860785560, 1563237055602189000, 70328294002955286540, 3163991615757072698400, 142344458748855549948960
Offset: 0

Views

Author

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

Keywords

Comments

The initial terms coincide with those of A170765, although the two sequences are eventually different.
Computed with MAGMA using commands similar to those used to compute A154638.

Links

Programs

  • GAP
    a:=[46,2070,93150,4190715];; for n in [5..20] do a[n]:=44*(a[n-1] +a[n-2] +a[n-3]) -990*a[n-4]; od; Concatenation([1], a); # G. C. Greubel, May 01 2019
  • Magma
    R:=PowerSeriesRing(Integers(), 30); Coefficients(R!( (1+x)*(1-x^4)/(1-45*x+1034*x^4-990*x^5) )); // G. C. Greubel, May 01 2019
  • Mathematica
    CoefficientList[Series[(t^4+2*t^3+2*t^2+2*t+1)/(990*t^4-44*t^3-44*t^2 - 44*t+1), {t,0,20}], t] (* or *) Join[{1}, LinearRecurrence[ {44, 44, 44, -990}, {46,2070,93150,4190715}, 20]] (* G. C. Greubel, Dec 11 2016 *)
coxG[{4, 990, -44}] (* The coxG program is at A169452 *) (* G. C. Greubel, May 01 2019 *)
  • PARI
    my(t='t+O('t^20)); Vec((t^4+2*t^3+2*t^2+2*t+1)/(990*t^4-44*t^3 - 44*t^2-44*t+1)) \\ G. C. Greubel, Dec 11 2016
  • Sage
    ((1+x)*(1-x^4)/(1-45*x+1034*x^4-990*x^5)).series(x, 30).coefficients(x, sparse=False) # G. C. Greubel, May 01 2019

Formula

G.f.: (t^4 + 2*t^3 + 2*t^2 + 2*t + 1)/(990*t^4 - 44*t^3 - 44*t^2 - 44*t + 1).
a(n) = 44*a(n-1)+44*a(n-2)+44*a(n-3)-990*a(n-4). - Wesley Ivan Hurt, May 10 2021

A163265 Number of reduced words of length n in Coxeter group on 47 generators S_i with relations (S_i)^2 = (S_i S_j)^4 = I.

Original entry on oeis.org

1, 47, 2162, 99452, 4573711, 210340980, 9673398765, 444871172700, 20459237269140, 940902479912925, 43271284508242650, 1990008638480367675, 91518761835509986350, 4208868045065726973000, 193562170919821248573375
Offset: 0

Views

Author

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

Keywords

Comments

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.

Links

Programs

  • GAP
    a:=[47,2162,99452,4573711];; for n in [5..20] do a[n]:=45*(a[n-1]+a[n-2] +a[n-3]-23*a[n-4]); od; Concatenation([1], a); # G. C. Greubel, May 01 2019
  • Magma
    R:=PowerSeriesRing(Integers(), 20); Coefficients(R!( (1+x)*(1-x^4)/(1-46*x+1080*x^4-1035*x^5) )); // G. C. Greubel, May 01 2019
  • Mathematica
    CoefficientList[Series[(t^4+2*t^3+2*t^2+2*t+1)/(1035*t^4-45*t^3-45*t^2 - 45*t+1), {t,0,20}], t] (* or *) LinearRecurrence[ {45, 45, 45, -1035}, {1,47,2162,99452,4573711}, 20] (* G. C. Greubel, Dec 12 2016 *)
coxG[{4, 1035, -45}] (* The coxG program is at A169452 *) (* G. C. Greubel, May 01 2019 *)
  • PARI
    my(t='t+O('t^20)); Vec((t^4+2*t^3+2*t^2+2*t+1)/(1035*t^4-45*t^3- 45*t^2-45*t+1)) \\ G. C. Greubel, Dec 12 2016
  • Sage
    ((1+x)*(1-x^4)/(1-46*x+1080*x^4-1035*x^5)).series(x, 20).coefficients(x, sparse=False) # G. C. Greubel, May 01 2019

Formula

G.f.: (t^4 + 2*t^3 + 2*t^2 + 2*t + 1)/(1035*t^4 - 45*t^3 - 45*t^2 - 45*t + 1).
a(n) = 45*a(n-1)+45*a(n-2)+45*a(n-3)-1035*a(n-4). - Wesley Ivan Hurt, May 10 2021

A163266 Number of reduced words of length n in Coxeter group on 48 generators S_i with relations (S_i)^2 = (S_i S_j)^4 = I.

Original entry on oeis.org

1, 48, 2256, 106032, 4982376, 234118656, 11001086208, 516933992448, 24290397127896, 1141390199234256, 53633194222120752, 2520189436004377296, 118422087020288430408, 5564578001118314478240, 261475955285477822620512, 12286587622406034842484384, 577338880885792093267553208
Offset: 0

Views

Author

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

Keywords

Comments

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.

Links

Programs

  • GAP
    a:=[48,2256,106032,4982376];; for n in [5..20] do a[n]:=46*(a[n-1] +a[n-2] +a[n-3]) -1081*a[n-4]; od; Concatenation([1], a); # G. C. Greubel, May 01 2019
  • Magma
    R:=PowerSeriesRing(Integers(), 20); Coefficients(R!( (1+x)*(1-x^4)/(1-47*x+1127*x^4-1081*x^5) )); // G. C. Greubel, May 01 2019
  • Mathematica
    CoefficientList[Series[(t^4+2*t^3+2*t^2+2*t+1)/(1081*t^4-46*t^3-46*t^2 - 46*t+1), {t,0,20}], t] (* or *) LinearRecurrence[ {46,46,46,-1081}, {1,48,2256,106032,4982376}, 20] (* G. C. Greubel, Dec 12 2016 *)
coxG[{4, 1081, -46}] (* The coxG program is at A169452 *) (* G. C. Greubel, May 01 2019 *)
  • PARI
    my(t='t+O('t^20)); Vec((t^4+2*t^3+2*t^2+2*t+1)/(1081*t^4-46*t^3 - 46*t^2-46*t+1)) \\ G. C. Greubel, Dec 12 2016
  • Sage
    ((1+x)*(1-x^4)/(1-47*x+1127*x^4-1081*x^5)).series(x, 20).coefficients(x, sparse=False) # G. C. Greubel, May 01 2019

Formula

G.f.: (t^4 + 2*t^3 + 2*t^2 + 2*t + 1)/(1081*t^4 - 46*t^3 - 46*t^2 - 46*t + 1).
a(n) = 46*a(n-1)+46*a(n-2)+46*a(n-3)-1081*a(n-4). - Wesley Ivan Hurt, May 10 2021

A163287 Number of reduced words of length n in Coxeter group on 49 generators S_i with relations (S_i)^2 = (S_i S_j)^4 = I.

Original entry on oeis.org

1, 49, 2352, 112896, 5417832, 259999488, 12477267096, 598778820864, 28735144795560, 1378987562102976, 66177035471527512, 3175808211876089664, 152405705797427455464, 7313885981134376257152, 350990324575741067673624
Offset: 0

Views

Author

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

Keywords

Comments

The initial terms coincide with those of A170768, although the two sequences are eventually different.
Computed with MAGMA using commands similar to those used to compute A154638.

Links

Programs

  • GAP
    a:=[49,2352,112896,5417832];; for n in [5..20] do a[n]:=47*(a[n-1]+a[n-2] +a[n-3] -24*a[n-4]); od; Concatenation([1], a); # G. C. Greubel, May 01 2019
  • Magma
    R:=PowerSeriesRing(Integers(), 20); Coefficients(R!( (1+x)*(1-x^4)/(1-48*x+1175*x^4-1128*x^5) )); // G. C. Greubel, May 01 2019
  • Mathematica
    CoefficientList[Series[(t^4+2*t^3+2*t^2+2*t+1)/(1128*t^4-47*t^3-47*t^2 - 47*t+1), {t,0,20}], t] (* or *) LinearRecurrence[{47, 47, 47, -1128}, {1,49,2352,112896,5417832}, 20] (* G. C. Greubel, Dec 17 2016 *)
coxG[{4, 1128, -47}] (* The coxG program is at A169452 *) (* G. C. Greubel, May 01 2019 *)
  • PARI
    my(t='t+O('t^20)); Vec((t^4+2*t^3+2*t^2+2*t+1)/(1128*t^4-47*t^3 - 47*t^2-47*t+1)) \\ G. C. Greubel, Dec 17 2016
  • Sage
    ((1+x)*(1-x^4)/(1-48*x+1175*x^4-1128*x^5)).series(x, 20).coefficients(x, sparse=False) # G. C. Greubel, May 01 2019

Formula

G.f.: (t^4 + 2*t^3 + 2*t^2 + 2*t + 1)/(1128*t^4 - 47*t^3 - 47*t^2 - 47*t + 1).
a(n) = 47*a(n-1)+47*a(n-2)+47*a(n-3)-1128*a(n-4). - Wesley Ivan Hurt, May 10 2021

A163315 Number of reduced words of length n in Coxeter group on 4 generators S_i with relations (S_i)^2 = (S_i S_j)^5 = I.

Original entry on oeis.org

1, 4, 12, 36, 108, 318, 936, 2760, 8136, 23976, 70662, 208260, 613788, 1808964, 5331420, 15712878, 46309320, 136483800, 402247944, 1185513624, 3493970742, 10297504260, 30349021740, 89445276900, 263615006412, 776931706398
Offset: 0

Views

Author

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

Keywords

Comments

The initial terms coincide with those of A003946, although the two sequences are eventually different.
Computed with MAGMA using commands similar to those used to compute A154638.

Links

Programs

  • Magma
    R:=PowerSeriesRing(Integers(), 30); Coefficients(R!( (1+x)*(1-x^5)/(1-3*x+5*x^5-3*x^6) )); // G. C. Greubel, May 12 2019
  • Mathematica
    CoefficientList[Series[(1+x)*(1-x^5)/(1-3*x+5*x^5-3*x^6), {x,0,30}], x] (* or *) Join[{1}, LinearRecurrence[{2,2,2,2,-3}, {1,4,12,36,108,318}, 30]] (* G. C. Greubel, Dec 18 2016 *)
coxG[{4, 3, -2}] (* The coxG program is at A169452 *) (* G. C. Greubel, May 12 2019 *)
  • PARI
    my(x='x+O('x^30)); Vec((1+x)*(1-x^5)/(1-3*x+5*x^5-3*x^6)) \\ G. C. Greubel, Dec 18 2016
  • Sage
    ((1+x)*(1-x^5)/(1-3*x+5*x^5-3*x^6)).series(x, 30).coefficients(x, sparse=False) # G. C. Greubel, May 12 2019

Formula

G.f.: (t^5 + 2*t^4 + 2*t^3 + 2*t^2 + 2*t + 1)/(3*t^5 - 2*t^4 - 2*t^3 - 2*t^2 - 2*t + 1).
a(n) = 2*a(n-1)+2*a(n-2)+2*a(n-3)+2*a(n-4)-3*a(n-5). - Wesley Ivan Hurt, May 10 2021
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