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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A167659 Number of reduced words of length n in Coxeter group on 10 generators S_i with relations (S_i)^2 = (S_i S_j)^15 = I.

Original entry on oeis.org

1, 10, 90, 810, 7290, 65610, 590490, 5314410, 47829690, 430467210, 3874204890, 34867844010, 313810596090, 2824295364810, 25418658283290, 228767924549565, 2058911320945680, 18530201888507520, 166771816996535280
Offset: 0

Views

Author

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

Keywords

Comments

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.

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)/(36*t^15 - 8*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 18 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)/(36*t^15 - 8*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).

A168687 Number of reduced words of length n in Coxeter group on 10 generators S_i with relations (S_i)^2 = (S_i S_j)^17 = I.

Original entry on oeis.org

1, 10, 90, 810, 7290, 65610, 590490, 5314410, 47829690, 430467210, 3874204890, 34867844010, 313810596090, 2824295364810, 25418658283290, 228767924549610, 2058911320946490, 18530201888518365, 166771816996664880
Offset: 0

Views

Author

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

Keywords

Comments

The initial terms coincide with those of A003952, although the two sequences are eventually different.
First disagreement at index 17: a(17) = 18530201888518365, A003952(17) = 18530201888518410. - Klaus Brockhaus, Mar 30 2011
Computed with MAGMA using commands similar to those used to compute A154638.

Links

Crossrefs

Cf. A003952 (g.f.: (1+x)/(1-9*x)).

Programs

  • Magma
    R:=PowerSeriesRing(Integers(), 40);
Coefficients(R!( (1+t)*(1-t^17)/(1 -9*t +44*t^17 -36*t^18) )); // G. C. Greubel, Mar 24 2021
  • Mathematica
    coxG[{17,36,-8}] (* The coxG program is at A169452 *) (* Harvey P. Dale, Dec 10 2015 *)
CoefficientList[Series[(1+t)*(1-t^17)/(1 -9*t +44*t^17 -36*t^18), {t, 0, 50}], t] (* G. C. Greubel, Aug 03 2016; Mar 24 2021 *)
  • Sage
    def A168687_list(prec):
    P. = PowerSeriesRing(ZZ, prec)
    return P( (1+t)*(1-t^17)/(1 -9*t +44*t^17 -36*t^18) ).list()
A168687_list(40) # G. C. Greubel, Mar 24 2021

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)/ (36*t^17 - 8*t^16 - 8*t^15 - 8*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).
G.f.: (1+t)*(1-t^17)/(1 -9 *t + 44*t^17 - 36*t^18). - G. C. Greubel, Mar 24 2021

A168735 Number of reduced words of length n in Coxeter group on 10 generators S_i with relations (S_i)^2 = (S_i S_j)^18 = I.

Original entry on oeis.org

1, 10, 90, 810, 7290, 65610, 590490, 5314410, 47829690, 430467210, 3874204890, 34867844010, 313810596090, 2824295364810, 25418658283290, 228767924549610, 2058911320946490, 18530201888518410, 166771816996665645
Offset: 0

Views

Author

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

Keywords

Comments

The initial terms coincide with those of A003952, although the two sequences are eventually different.
First disagreement at index 18: a(18) = 166771816996665645, A003952(18) = 166771816996665690. - Klaus Brockhaus, Mar 27 2011
Computed with MAGMA using commands similar to those used to compute A154638.

Links

Crossrefs

Cf. A003952 (G.f.: (1+x)/(1-9*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)/(36*t^18 - 8*t^17 - 8*t^16 - 8*t^15 - 8*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, Aug 08 2016 *)
coxG[{18,36,-8}] (* The coxG program is at A169452 *) (* Harvey P. Dale, Oct 22 2022 *)

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)/(36*t^18 - 8*t^17 - 8*t^16 - 8*t^15 - 8*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).

A168783 Number of reduced words of length n in Coxeter group on 10 generators S_i with relations (S_i)^2 = (S_i S_j)^19 = I.

Original entry on oeis.org

1, 10, 90, 810, 7290, 65610, 590490, 5314410, 47829690, 430467210, 3874204890, 34867844010, 313810596090, 2824295364810, 25418658283290, 228767924549610, 2058911320946490, 18530201888518410, 166771816996665690
Offset: 0

Views

Author

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

Keywords

Comments

The initial terms coincide with those of A003952, although the two sequences are eventually different.
First disagreement at index 19: a(19) = 1500946352969991165, A003952(19) = 1500946352969991210. - Klaus Brockhaus, Mar 25 2011
Computed with MAGMA using commands similar to those used to compute A154638.

Links

Crossrefs

Cf. A003952 (G.f.: (1+x)/(1-9*x)).

Programs

  • Mathematica
    coxG[{19,36,-8}] (* The coxG program is at A169452 *) (* Harvey P. Dale, Oct 09 2014 *)
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)/(36*t^19 - 8*t^18 - 8*t^17 - 8*t^16 - 8*t^15 - 8*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, Aug 12 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)/(36*t^19 - 8*t^18 - 8*t^17 - 8*t^16 - 8*t^15 - 8*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).

A168831 Number of reduced words of length n in Coxeter group on 10 generators S_i with relations (S_i)^2 = (S_i S_j)^20 = I.

Original entry on oeis.org

1, 10, 90, 810, 7290, 65610, 590490, 5314410, 47829690, 430467210, 3874204890, 34867844010, 313810596090, 2824295364810, 25418658283290, 228767924549610, 2058911320946490, 18530201888518410, 166771816996665690
Offset: 0

Views

Author

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

Keywords

Comments

The initial terms coincide with those of A003952, although the two sequences are eventually different.
First disagreement at index 20: a(20) = 13508517176729920845, A003952(20) = 13508517176729920890. - Klaus Brockhaus, Apr 01 2011
Computed with MAGMA using commands similar to those used to compute A154638.

Links

Crossrefs

Cf. A003952 (G.f.: (1+x)/(1-9*x)).

Programs

  • Mathematica
    CoefficientList[Series[(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)/(36*t^20 - 8*t^19 - 8*t^18 - 8*t^17 - 8*t^16 - 8*t^15 - 8*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,0,100}], t] (* G. C. Greubel, Nov 22 2016 *)

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)/(36*t^20 - 8*t^19 - 8*t^18 - 8*t^17 - 8*t^16 - 8*t^15 - 8*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).

A170691 Number of reduced words of length n in Coxeter group on 10 generators S_i with relations (S_i)^2 = (S_i S_j)^50 = I.

Original entry on oeis.org

1, 10, 90, 810, 7290, 65610, 590490, 5314410, 47829690, 430467210, 3874204890, 34867844010, 313810596090, 2824295364810, 25418658283290, 228767924549610, 2058911320946490, 18530201888518410, 166771816996665690
Offset: 0

Views

Author

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

Keywords

Comments

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.
About the initial comment, first disagreement is at index 50 and the difference is 45. - Vincenzo Librandi, Dec 08 2012

Links

Programs

  • Mathematica
    With[{num=Total[2t^Range[49]]+t^50+1,den=Total[-8 t^Range[49]]+ 36 t^50+1},CoefficientList[Series[num/den,{t,0,30}],t]] (* Harvey P. Dale, Aug 11 2012 *)

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)/(36*t^50 - 8*t^49 - 8*t^48 - 8*t^47 - 8*t^46 - 8*t^45 - 8*t^44
- 8*t^43 - 8*t^42 - 8*t^41 - 8*t^40 - 8*t^39 - 8*t^38 - 8*t^37 - 8*t^36
- 8*t^35 - 8*t^34 - 8*t^33 - 8*t^32 - 8*t^31 - 8*t^30 - 8*t^29 - 8*t^28
- 8*t^27 - 8*t^26 - 8*t^25 - 8*t^24 - 8*t^23 - 8*t^22 - 8*t^21 - 8*t^20
- 8*t^19 - 8*t^18 - 8*t^17 - 8*t^16 - 8*t^15 - 8*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).

A162756 Number of reduced words of length n in Coxeter group on 10 generators S_i with relations (S_i)^2 = (S_i S_j)^3 = I.

Original entry on oeis.org

1, 10, 90, 765, 6480, 54720, 462060, 3900960, 32934240, 278047440, 2347418880, 19818097920, 167314426560, 1412553116160, 11925488816640, 100681016106240, 850000127201280, 7176131549061120, 60584536830274560, 511485342455439360
Offset: 0

Views

Author

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

Keywords

Comments

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.

Links

Formula

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

A165219 Number of reduced words of length n in Coxeter group on 10 generators S_i with relations (S_i)^2 = (S_i S_j)^9 = I.

Original entry on oeis.org

1, 10, 90, 810, 7290, 65610, 590490, 5314410, 47829690, 430467165, 3874204080, 34867833120, 313810465680, 2824293899520, 25418642471280, 228767758621920, 2058909615020880, 18530184622000320, 166771644379316460
Offset: 0

Views

Author

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

Keywords

Comments

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.

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)/(36*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)

A168879 Number of reduced words of length n in Coxeter group on 10 generators S_i with relations (S_i)^2 = (S_i S_j)^21 = I.

Original entry on oeis.org

1, 10, 90, 810, 7290, 65610, 590490, 5314410, 47829690, 430467210, 3874204890, 34867844010, 313810596090, 2824295364810, 25418658283290, 228767924549610, 2058911320946490, 18530201888518410, 166771816996665690
Offset: 0

Views

Author

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

Keywords

Comments

The initial terms coincide with those of A003952, although the two sequences are eventually different.
First disagreement at index 21: a(21) = 121576654590569287965, A003952(21) = 121576654590569288010. - Klaus Brockhaus, Apr 05 2011
Computed with MAGMA using commands similar to those used to compute A154638.

Links

Crossrefs

Cf. A003952 (G.f.: (1+x)/(1-9*x)).

Formula

G.f.: (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)/(36*t^21 - 8*t^20 - 8*t^19 - 8*t^18 - 8*t^17 - 8*t^16 - 8*t^15 - 8*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).

A168927 Number of reduced words of length n in Coxeter group on 10 generators S_i with relations (S_i)^2 = (S_i S_j)^22 = I.

Original entry on oeis.org

1, 10, 90, 810, 7290, 65610, 590490, 5314410, 47829690, 430467210, 3874204890, 34867844010, 313810596090, 2824295364810, 25418658283290, 228767924549610, 2058911320946490, 18530201888518410, 166771816996665690
Offset: 0

Views

Author

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

Keywords

Comments

The initial terms coincide with those of A003952, although the two sequences are eventually different.
First disagreement at index 22: a(22) = 1094189891315123592045, A003952(22) = 1094189891315123592090. - Klaus Brockhaus, Apr 09 2011
Computed with MAGMA using commands similar to those used to compute A154638.

Links

Crossrefs

Cf. A003952 (G.f.: (1+x)/(1-9*x)).

Programs

Formula

G.f.: (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)/(36*t^22 - 8*t^21 - 8*t^20 - 8*t^19 - 8*t^18 - 8*t^17 - 8*t^16 - 8*t^15 - 8*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).
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Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

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