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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A167757 Number of reduced words of length n in Coxeter group on 32 generators S_i with relations (S_i)^2 = (S_i S_j)^15 = I.

Original entry on oeis.org

1, 32, 992, 30752, 953312, 29552672, 916132832, 28400117792, 880403651552, 27292513198112, 846067909141472, 26228105183385632, 813071260684954592, 25205209081233592352, 781361481518241362912, 24222205927065482249776
Offset: 0

Views

Author

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

Keywords

Comments

The initial terms coincide with those of A170751, although the two sequences are eventually different.
Computed with MAGMA using commands similar to those used to compute A154638.

Links

Programs

  • Mathematica
    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)/(465*t^15 - 30*t^14 - 30*t^13 - 30*t^12 - 30*t^11 - 30*t^10 - 30*t^9 - 30*t^8 - 30*t^7 - 30*t^6 - 30*t^5 - 30*t^4 - 30*t^3 - 30*t^2 - 30*t + 1), {t, 0, 50}], t] (* G. C. Greubel, Jun 23 2016 *)

Formula

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)/(465*t^15 - 30*t^14 - 30*t^13 - 30*t^12 - 30*t^11 - 30*t^10 - 30*t^9 - 30*t^8 - 30*t^7 - 30*t^6 - 30*t^5 - 30*t^4 - 30*t^3 - 30*t^2 - 30*t + 1).

A168709 Number of reduced words of length n in Coxeter group on 32 generators S_i with relations (S_i)^2 = (S_i S_j)^17 = I.

Original entry on oeis.org

1, 32, 992, 30752, 953312, 29552672, 916132832, 28400117792, 880403651552, 27292513198112, 846067909141472, 26228105183385632, 813071260684954592, 25205209081233592352, 781361481518241362912, 24222205927065482250272
Offset: 0

Views

Author

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

Keywords

Comments

The initial terms coincide with those of A170751, although the two sequences are eventually different.
First disagreement at index 17: a(17) = 23277539895909928442510896, A170751(17) = 23277539895909928442511392. - Klaus Brockhaus, Mar 28 2011
Computed with MAGMA using commands similar to those used to compute A154638.

Links

Crossrefs

Cf. A170751 (G.f.: (1+x)/(1-31*x)).

Programs

  • Mathematica
    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)/(465*t^17 - 30*t^16 - 30*t^15 - 30*t^14 - 30*t^13 - 30*t^12 - 30*t^11 - 30*t^10 - 30*t^9 - 30*t^8 - 30*t^7 - 30*t^6 - 30*t^5 - 30*t^4 - 30*t^3 - 30*t^2 - 30*t + 1), {t,0,50}], t] (* G. C. Greubel, Aug 05 2016 *)
coxG[{17,465,-30}] (* The coxG program is at A169452 *) (* Harvey P. Dale, Oct 30 2023 *)

Formula

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)/(465*t^17 - 30*t^16 - 30*t^15 - 30*t^14 - 30*t^13 - 30*t^12 - 30*t^11 - 30*t^10 - 30*t^9 - 30*t^8 - 30*t^7 - 30*t^6 - 30*t^5 - 30*t^4 - 30*t^3 - 30*t^2 - 30*t + 1).

A168757 Number of reduced words of length n in Coxeter group on 32 generators S_i with relations (S_i)^2 = (S_i S_j)^18 = I.

Original entry on oeis.org

1, 32, 992, 30752, 953312, 29552672, 916132832, 28400117792, 880403651552, 27292513198112, 846067909141472, 26228105183385632, 813071260684954592, 25205209081233592352, 781361481518241362912, 24222205927065482250272
Offset: 0

Views

Author

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

Keywords

Comments

The initial terms coincide with those of A170751, although the two sequences are eventually different.
First disagreement at index 18: a(18) = 721603736773207781717852656, A170751(18) = 721603736773207781717853152. - Klaus Brockhaus, Mar 26 2011
Computed with MAGMA using commands similar to those used to compute A154638.

Links

Crossrefs

Cf. A170751 (G.f.: (1+x)/(1-31*x)).

Programs

  • Mathematica
    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)/(465*t^18 - 30*t^17 - 30*t^16 - 30*t^15 - 30*t^14 - 30*t^13 - 30*t^12 - 30*t^11 - 30*t^10 - 30*t^9 - 30*t^8 - 30*t^7 - 30*t^6 - 30*t^5 - 30*t^4 - 30*t^3 - 30*t^2 - 30*t + 1), {t, 0, 50}], t] (* G. C. Greubel, Aug 11 2016 *)

Formula

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)/(465*t^18 - 30*t^17 - 30*t^16 - 30*t^15 - 30*t^14 - 30*t^13 - 30*t^12 - 30*t^11 - 30*t^10 - 30*t^9 - 30*t^8 - 30*t^7 - 30*t^6 - 30*t^5 - 30*t^4 - 30*t^3 - 30*t^2 - 30*t + 1).

A168805 Number of reduced words of length n in Coxeter group on 32 generators S_i with relations (S_i)^2 = (S_i S_j)^19 = I.

Original entry on oeis.org

1, 32, 992, 30752, 953312, 29552672, 916132832, 28400117792, 880403651552, 27292513198112, 846067909141472, 26228105183385632, 813071260684954592, 25205209081233592352, 781361481518241362912, 24222205927065482250272
Offset: 0

Views

Author

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

Keywords

Comments

The initial terms coincide with those of A170751, although the two sequences are eventually different.
First disagreement at index 19: a(19) = 22369715839969441233253447216, A170751(19) = 22369715839969441233253447712. - Klaus Brockhaus, Apr 01 2011
Computed with MAGMA using commands similar to those used to compute A154638.

Links

Crossrefs

Cf. A170751 (G.f.: (1+x)/(1-31*x)).

Programs

  • Mathematica
    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)/(465*t^19 - 30*t^18 - 30*t^17 - 30*t^16 - 30*t^15 - 30*t^14 - 30*t^13 - 30*t^12 - 30*t^11 - 30*t^10 - 30*t^9 - 30*t^8 - 30*t^7 - 30*t^6 - 30*t^5 - 30*t^4 - 30*t^3 - 30*t^2 - 30*t + 1), {t, 0, 50}], t] (* G. C. Greubel, Aug 16 2016 *)

Formula

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)/(465*t^19 - 30*t^18 - 30*t^17 - 30*t^16 - 30*t^15 - 30*t^14 - 30*t^13 - 30*t^12 - 30*t^11 - 30*t^10 - 30*t^9 - 30*t^8 - 30*t^7 - 30*t^6 - 30*t^5 - 30*t^4 - 30*t^3 - 30*t^2 - 30*t + 1).

A170713 Number of reduced words of length n in Coxeter group on 32 generators S_i with relations (S_i)^2 = (S_i S_j)^50 = I.

Original entry on oeis.org

1, 32, 992, 30752, 953312, 29552672, 916132832, 28400117792, 880403651552, 27292513198112, 846067909141472, 26228105183385632, 813071260684954592, 25205209081233592352, 781361481518241362912, 24222205927065482250272
Offset: 0

Views

Author

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

Keywords

Comments

The initial terms coincide with those of A170751, 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 496. - Vincenzo Librandi, Dec 06 2012

Links

Programs

  • Mathematica
    With[{num = Total[2 t^Range[49]] + t^50 + 1, den = Total[-30 t^Range[49]] + 465 t^50 + 1}, CoefficientList[Series[num/den, {t, 0, 30}], t]] (* Vincenzo Librandi, Dec 06 2012 *)
coxG[{50,465,-30}] (* The coxG program is at A169452 *) (* Harvey P. Dale, Nov 15 2018 *)

Formula

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)/(465*t^50 - 30*t^49 - 30*t^48 - 30*t^47 - 30*t^46 - 30*t^45 -
30*t^44 - 30*t^43 - 30*t^42 - 30*t^41 - 30*t^40 - 30*t^39 - 30*t^38 -
30*t^37 - 30*t^36 - 30*t^35 - 30*t^34 - 30*t^33 - 30*t^32 - 30*t^31 -
30*t^30 - 30*t^29 - 30*t^28 - 30*t^27 - 30*t^26 - 30*t^25 - 30*t^24 -
30*t^23 - 30*t^22 - 30*t^21 - 30*t^20 - 30*t^19 - 30*t^18 - 30*t^17 -
30*t^16 - 30*t^15 - 30*t^14 - 30*t^13 - 30*t^12 - 30*t^11 - 30*t^10 -
30*t^9 - 30*t^8 - 30*t^7 - 30*t^6 - 30*t^5 - 30*t^4 - 30*t^3 - 30*t^2 -
30*t + 1).

A162836 Number of reduced words of length n in Coxeter group on 32 generators S_i with relations (S_i)^2 = (S_i S_j)^3 = I.

Original entry on oeis.org

1, 32, 992, 30256, 922560, 28123200, 857303760, 26133818400, 796656376800, 24285059607600, 740299253976000, 22567084192296000, 687928950670626000, 20970641892788820000, 639263431154365740000, 19487135229352795710000
Offset: 0

Views

Author

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

Keywords

Comments

The initial terms coincide with those of A170751, although the two sequences are eventually different.
Computed with MAGMA using commands similar to those used to compute A154638.

Links

Formula

G.f.: (t^3 + 2*t^2 + 2*t + 1)/(465*t^3 - 30*t^2 - 30*t + 1)

A164668 Number of reduced words of length n in Coxeter group on 32 generators S_i with relations (S_i)^2 = (S_i S_j)^7 = I.

Original entry on oeis.org

1, 32, 992, 30752, 953312, 29552672, 916132832, 28400117296, 880403620800, 27292511768640, 846067850066880, 26228102894483520, 813071175543706560, 25205206002111144000, 781361372433389169360, 24222202122841326496800
Offset: 0

Views

Author

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

Keywords

Comments

The initial terms coincide with those of A170751, although the two sequences are eventually different.
Computed with MAGMA using commands similar to those used to compute A154638.

Links

Programs

Formula

G.f.: (t^7 + 2*t^6 + 2*t^5 + 2*t^4 + 2*t^3 + 2*t^2 + 2*t + 1)/(465*t^7 - 30*t^6 - 30*t^5 - 30*t^4 - 30*t^3 - 30*t^2 - 30*t + 1).

A165131 Number of reduced words of length n in Coxeter group on 32 generators S_i with relations (S_i)^2 = (S_i S_j)^8 = I.

Original entry on oeis.org

1, 32, 992, 30752, 953312, 29552672, 916132832, 28400117792, 880403651056, 27292513167360, 846067907712000, 26228105124311040, 813071258396052480, 25205208996092344320, 781361478439118914560, 24222205817980629811200
Offset: 0

Views

Author

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

Keywords

Comments

The initial terms coincide with those of A170751, although the two sequences are eventually different.
Computed with MAGMA using commands similar to those used to compute A154638.

Links

Programs

Formula

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)/(465*t^8 -
30*t^7 - 30*t^6 - 30*t^5 - 30*t^4 - 30*t^3 - 30*t^2 - 30*t + 1)

A165548 Number of reduced words of length n in Coxeter group on 32 generators S_i with relations (S_i)^2 = (S_i S_j)^9 = I.

Original entry on oeis.org

1, 32, 992, 30752, 953312, 29552672, 916132832, 28400117792, 880403651552, 27292513197616, 846067909110720, 26228105181956160, 813071260625880000, 25205209078944690240, 781361481433100114880, 24222205923986359801920
Offset: 0

Views

Author

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

Keywords

Comments

The initial terms coincide with those of A170751, although the two sequences are eventually different.
Computed with MAGMA using commands similar to those used to compute A154638.

Links

Formula

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)/(465*t^9 - 30*t^8 - 30*t^7 - 30*t^6 - 30*t^5 - 30*t^4 - 30*t^3 -
30*t^2 - 30*t + 1)

A168853 Number of reduced words of length n in Coxeter group on 32 generators S_i with relations (S_i)^2 = (S_i S_j)^20 = I.

Original entry on oeis.org

1, 32, 992, 30752, 953312, 29552672, 916132832, 28400117792, 880403651552, 27292513198112, 846067909141472, 26228105183385632, 813071260684954592, 25205209081233592352, 781361481518241362912, 24222205927065482250272
Offset: 0

Views

Author

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

Keywords

Comments

The initial terms coincide with those of A170751, although the two sequences are eventually different.
First disagreement at index 20: a(20) = 693461191039052678230856878576, A170751(20) = 693461191039052678230856879072. - Klaus Brockhaus, Apr 04 2011
Computed with MAGMA using commands similar to those used to compute A154638.

Links

Crossrefs

Cf. A170751 (G.f.: (1+x)/(1-31*x)).

Programs

Formula

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)/(465*t^20 - 30*t^19 - 30*t^18 - 30*t^17 - 30*t^16 - 30*t^15 - 30*t^14 - 30*t^13 - 30*t^12 - 30*t^11 - 30*t^10 - 30*t^9 - 30*t^8 - 30*t^7 - 30*t^6 - 30*t^5 - 30*t^4 - 30*t^3 - 30*t^2 - 30*t + 1).
Previous Showing 11-20 of 49 results. Next

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