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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A167863 Number of reduced words of length n in Coxeter group on 48 generators S_i with relations (S_i)^2 = (S_i S_j)^15 = I.

Original entry on oeis.org

1, 48, 2256, 106032, 4983504, 234224688, 11008560336, 517402335792, 24317909782224, 1142941759764528, 53718262708932816, 2524758347319842352, 118663642324032590544, 5577191189229531755568, 262127985893787992511696
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

  • Mathematica
    coxG[{15,1081,-46}] (* The coxG program is at A169452 *) (* Harvey P. Dale, Jun 05 2016 *)
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)/(1081*t^15 - 46*t^14 - 46*t^13 - 46*t^12 - 46*t^11 - 46*t^10 - 46*t^9 - 46*t^8 - 46*t^7 - 46*t^6 - 46*t^5 - 46*t^4 - 46*t^3 - 46*t^2 - 46*t + 1), {t, 0, 50}], t] (* G. C. Greubel, Jun 28 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)/(1081*t^15 - 46*t^14 - 46*t^13 - 46*t^12 - 46*t^11 - 46*t^10 - 46*t^9 - 46*t^8 - 46*t^7 - 46*t^6 - 46*t^5 - 46*t^4 - 46*t^3 - 46*t^2 - 46*t + 1).

A168725 Number of reduced words of length n in Coxeter group on 48 generators S_i with relations (S_i)^2 = (S_i S_j)^17 = I.

Original entry on oeis.org

1, 48, 2256, 106032, 4983504, 234224688, 11008560336, 517402335792, 24317909782224, 1142941759764528, 53718262708932816, 2524758347319842352, 118663642324032590544, 5577191189229531755568, 262127985893787992511696
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.
First disagreement at index 17: a(17) = 27214913879450750746541812680, A170767(17) = 27214913879450750746541813808. - Klaus Brockhaus, Mar 28 2011
Computed with MAGMA using commands similar to those used to compute A154638.

Links

Crossrefs

Cf. A170767 (G.f.: (1+x)/(1-47*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)/(1081*t^17 - 46*t^16 - 46*t^15 - 46*t^14 - 46*t^13 - 46*t^12 - 46*t^11 - 46*t^10 - 46*t^9 - 46*t^8 - 46*t^7 - 46*t^6 - 46*t^5 - 46*t^4 - 46*t^3 - 46*t^2 - 46*t + 1), {t,0,50}], t] (* G. C. Greubel, Aug 06 2016 *)
coxG[{17,1081,-46}] (* The coxG program is at A169452 *) (* Harvey P. Dale, Mar 10 2019 *)

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)/(1081*t^17 - 46*t^16 - 46*t^15 - 46*t^14 - 46*t^13 - 46*t^12 - 46*t^11 - 46*t^10 - 46*t^9 - 46*t^8 - 46*t^7 - 46*t^6 - 46*t^5 - 46*t^4 - 46*t^3 - 46*t^2 - 46*t + 1).

A168773 Number of reduced words of length n in Coxeter group on 48 generators S_i with relations (S_i)^2 = (S_i S_j)^18 = I.

Original entry on oeis.org

1, 48, 2256, 106032, 4983504, 234224688, 11008560336, 517402335792, 24317909782224, 1142941759764528, 53718262708932816, 2524758347319842352, 118663642324032590544, 5577191189229531755568, 262127985893787992511696
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.
First disagreement at index 18: a(18) = 1279100952334185285087465247848, A170767(18) = 1279100952334185285087465248976. - Klaus Brockhaus, Mar 25 2011
Computed with MAGMA using commands similar to those used to compute A154638.

Links

Crossrefs

Cf. A170767 (G.f.: (1+x)/(1-47*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)/(1081*t^18 - 46*t^17 - 46*t^16 - 46*t^15 - 46*t^14 - 46*t^13 - 46*t^12 - 46*t^11 - 46*t^10 - 46*t^9 - 46*t^8 - 46*t^7 - 46*t^6 - 46*t^5 - 46*t^4 - 46*t^3 - 46*t^2 - 46*t + 1), {t, 0, 50}], t] (* G. C. Greubel, Aug 12 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)/(1081*t^18 - 46*t^17 - 46*t^16 - 46*t^15 - 46*t^14 - 46*t^13 - 46*t^12 - 46*t^11 - 46*t^10 - 46*t^9 - 46*t^8 - 46*t^7 - 46*t^6 - 46*t^5 - 46*t^4 - 46*t^3 - 46*t^2 - 46*t + 1).

A168821 Number of reduced words of length n in Coxeter group on 48 generators S_i with relations (S_i)^2 = (S_i S_j)^19 = I.

Original entry on oeis.org

1, 48, 2256, 106032, 4983504, 234224688, 11008560336, 517402335792, 24317909782224, 1142941759764528, 53718262708932816, 2524758347319842352, 118663642324032590544, 5577191189229531755568, 262127985893787992511696
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.
First disagreement at index 19: a(19) = 60117744759706708399110866700744, A170767(19) = 60117744759706708399110866701872. - Klaus Brockhaus, Apr 01 2011
Computed with MAGMA using commands similar to those used to compute A154638.

Links

Crossrefs

Cf. A170767 (G.f.: (1+x)/(1-47*x)).

Programs

  • Mathematica
    coxG[{19,1081,-46}] (* The coxG program is at A169452 *) (* Harvey P. Dale, Feb 06 2015 *)
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)/(1081*t^19 - 46*t^18 - 46*t^17 - 46*t^16 - 46*t^15 - 46*t^14 - 46*t^13 - 46*t^12 - 46*t^11 - 46*t^10 - 46*t^9 - 46*t^8 - 46*t^7 - 46*t^6 - 46*t^5 - 46*t^4 - 46*t^3 - 46*t^2 - 46*t + 1), {t,0,50}], t] (* G. C. Greubel, Nov 21 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)/(1081*t^19 - 46*t^18 - 46*t^17 - 46*t^16 - 46*t^15 - 46*t^14 - 46*t^13 - 46*t^12 - 46*t^11 - 46*t^10 - 46*t^9 - 46*t^8 - 46*t^7 - 46*t^6 - 46*t^5 - 46*t^4 - 46*t^3 - 46*t^2 - 46*t + 1).

A170729 Number of reduced words of length n in Coxeter group on 48 generators S_i with relations (S_i)^2 = (S_i S_j)^50 = I.

Original entry on oeis.org

1, 48, 2256, 106032, 4983504, 234224688, 11008560336, 517402335792, 24317909782224, 1142941759764528, 53718262708932816, 2524758347319842352, 118663642324032590544, 5577191189229531755568, 262127985893787992511696
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.
About the initial comment, first disagreement is at index 50 and the difference is 1128. - Vincenzo Librandi, Dec 08 2012

Links

Programs

  • Mathematica
    With[{num = Total[2 t^Range[49]] + t^50 + 1, den = Total[-46 t^Range[49]] + 1081 t^50 + 1}, CoefficientList[Series[num/den, {t, 0, 20}], t]] (* Vincenzo Librandi, Dec 08 2012 *)
coxG[{50,1081,-46}] (* The coxG program is at A169452 *) (* Harvey P. Dale, Jul 07 2024 *)

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)/(1081*t^50 - 46*t^49 - 46*t^48 - 46*t^47 - 46*t^46 - 46*t^45 -
46*t^44 - 46*t^43 - 46*t^42 - 46*t^41 - 46*t^40 - 46*t^39 - 46*t^38 -
46*t^37 - 46*t^36 - 46*t^35 - 46*t^34 - 46*t^33 - 46*t^32 - 46*t^31 -
46*t^30 - 46*t^29 - 46*t^28 - 46*t^27 - 46*t^26 - 46*t^25 - 46*t^24 -
46*t^23 - 46*t^22 - 46*t^21 - 46*t^20 - 46*t^19 - 46*t^18 - 46*t^17 -
46*t^16 - 46*t^15 - 46*t^14 - 46*t^13 - 46*t^12 - 46*t^11 - 46*t^10 -
46*t^9 - 46*t^8 - 46*t^7 - 46*t^6 - 46*t^5 - 46*t^4 - 46*t^3 - 46*t^2 -
46*t + 1)

A162913 Number of reduced words of length n in Coxeter group on 48 generators S_i with relations (S_i)^2 = (S_i S_j)^3 = I.

Original entry on oeis.org

1, 48, 2256, 104904, 4877472, 226750560, 10541488248, 490066437936, 22782847249104, 1059158680807752, 49239548471206560, 2289112271116376928, 106419233167075660536, 4947355938259459431984, 229999127520543810796752
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

  • Mathematica
    coxG[{3,1081,-46}] (* The coxG program is at A169452 *) (* or *) LinearRecurrence[{46,46,-1081},{1,48,2256,104904},30] (* Harvey P. Dale, Dec 30 2017 *)

Formula

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

A164693 Number of reduced words of length n in Coxeter group on 48 generators S_i with relations (S_i)^2 = (S_i S_j)^7 = I.

Original entry on oeis.org

1, 48, 2256, 106032, 4983504, 234224688, 11008560336, 517402334664, 24317909676192, 1142941752290400, 53718262240589472, 2524758319805916768, 118663640772294032544, 5577191104144368918624, 262127981323573161732216
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

Formula

G.f.: (t^7 + 2*t^6 + 2*t^5 + 2*t^4 + 2*t^3 + 2*t^2 + 2*t + 1)/(1081*t^7 - 46*t^6 - 46*t^5 - 46*t^4 - 46*t^3 - 46*t^2 - 46*t + 1).

A165180 Number of reduced words of length n in Coxeter group on 48 generators S_i with relations (S_i)^2 = (S_i S_j)^8 = I.

Original entry on oeis.org

1, 48, 2256, 106032, 4983504, 234224688, 11008560336, 517402335792, 24317909781096, 1142941759658496, 53718262701458688, 2524758346851499008, 118663642296518664960, 5577191187677793197568, 262127985808702829674752
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

  • Mathematica
    With[{num=Total[2t^Range[7]]+t^8+1,den=Total[-46 t^Range[7]]+1081t^8+ 1}, CoefficientList[Series[num/den,{t,0,30}],t]] (* Harvey P. Dale, Jul 27 2011 *)

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)/(1081*t^8 - 46*t^7 - 46*t^6 - 46*t^5 - 46*t^4 - 46*t^3 - 46*t^2 - 46*t + 1).
a(n) = -1081*a(n-8) + 46*Sum_{k=1..7} a(n-k). - Wesley Ivan Hurt, Sep 04 2022

A165708 Number of reduced words of length n in Coxeter group on 48 generators S_i with relations (S_i)^2 = (S_i S_j)^9 = I.

Original entry on oeis.org

1, 48, 2256, 106032, 4983504, 234224688, 11008560336, 517402335792, 24317909782224, 1142941759763400, 53718262708826784, 2524758347312368224, 118663642323564247200, 5577191189202017829984, 262127985892236253953696
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

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)/(1081*t^9 - 46*t^8 - 46*t^7 - 46*t^6 - 46*t^5 - 46*t^4 - 46*t^3 -
46*t^2 - 46*t + 1)

A168869 Number of reduced words of length n in Coxeter group on 48 generators S_i with relations (S_i)^2 = (S_i S_j)^20 = I.

Original entry on oeis.org

1, 48, 2256, 106032, 4983504, 234224688, 11008560336, 517402335792, 24317909782224, 1142941759764528, 53718262708932816, 2524758347319842352, 118663642324032590544, 5577191189229531755568, 262127985893787992511696
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.
First disagreement at index 20: a(20) = 2825534003706215294758210734986856, A170767(20) = 2825534003706215294758210734987984. - Klaus Brockhaus, Apr 04 2011
Computed with MAGMA using commands similar to those used to compute A154638.

Links

Crossrefs

Cf. A170767 (G.f.: (1+x)/(1-47*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)/(1081*t^20 - 46*t^19 - 46*t^18 - 46*t^17 - 46*t^16 - 46*t^15 - 46*t^14 - 46*t^13 - 46*t^12 - 46*t^11 - 46*t^10 - 46*t^9 - 46*t^8 - 46*t^7 - 46*t^6 - 46*t^5 - 46*t^4 - 46*t^3 - 46*t^2 - 46*t + 1).
Previous Showing 11-20 of 49 results. Next

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

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