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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A167952 Number of reduced words of length n in Coxeter group on 36 generators S_i with relations (S_i)^2 = (S_i S_j)^16 = I.

Original entry on oeis.org

1, 36, 1260, 44100, 1543500, 54022500, 1890787500, 66177562500, 2316214687500, 81067514062500, 2837362992187500, 99307704726562500, 3475769665429687500, 121651938290039062500, 4257817840151367187500, 149023624405297851562500
Offset: 0

Views

Author

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

Keywords

Comments

The initial terms coincide with those of A170755, although the two sequences are eventually different.
Computed with MAGMA using commands similar to those used to compute A154638.

Links

Crossrefs

Cf. A154638, A169452, A170755.

Programs

  • Magma
    R:=PowerSeriesRing(Integers(), 40); Coefficients(R!( (1+x)*(1-x^16)/(1-35*x+629*x^16-595*x^17) )); // G. C. Greubel, Sep 06 2023
  • Mathematica
    coxG[{16,595,-34}] (* The coxG program is at A169452 *) (* Harvey P. Dale, Apr 07 2015 *)
CoefficientList[Series[(1+t)*(1-t^16)/(1-35*t+629*t^16-595*t^17), {t, 0, 50}], t] (* G. C. Greubel, Jul 02 2016; Sep 06 2023 *)
  • SageMath
    def A167955_list(prec):
    P. = PowerSeriesRing(ZZ, prec)
    return P( (1+x)*(1-x^16)/(1-35*x+629*x^16-595*x^17) ).list()
A167955_list(40) # G. C. Greubel, Sep 06 2023

Formula

G.f.: (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)/( 595*t^16 - 34*t^15 - 34*t^14 - 34*t^13 - 34*t^12 - 34*t^11 - 34*t^10 - 34*t^9 - 34*t^8 - 34*t^7 - 34*t^6 - 34*t^5 - 34*t^4 - 34*t^3 - 34*t^2 - 34*t + 1).
From G. C. Greubel, Sep 06 2023: (Start)
G.f.: (1+t)*(1-t^16)/(1 - 35*t + 629*t^16 - 595*t^17).
a(n) = 34*Sum_{j=1..15} a(n-j) - 595*a(n-16). (End)

A168713 Number of reduced words of length n in Coxeter group on 36 generators S_i with relations (S_i)^2 = (S_i S_j)^17 = I.

Original entry on oeis.org

1, 36, 1260, 44100, 1543500, 54022500, 1890787500, 66177562500, 2316214687500, 81067514062500, 2837362992187500, 99307704726562500, 3475769665429687500, 121651938290039062500, 4257817840151367187500, 149023624405297851562500
Offset: 0

Views

Author

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

Keywords

Comments

The initial terms coincide with those of A170755, although the two sequences are eventually different.
First disagreement at index 17: a(17) = 182553939896489868164061870, A170755(17) = 182553939896489868164062500. - Klaus Brockhaus, Mar 28 2011
Computed with MAGMA using commands similar to those used to compute A154638.

Links

Crossrefs

Cf. A170755 (G.f.: (1+x)/(1-35*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)/(595*t^17 - 34*t^16 - 34*t^15 - 34*t^14 - 34*t^13 - 34*t^12 - 34*t^11 - 34*t^10 - 34*t^9 - 34*t^8 - 34*t^7 - 34*t^6 - 34*t^5 - 34*t^4 - 34*t^3 - 34*t^2 - 34*t + 1), {t,0,50}], t] (* G. C. Greubel, Aug 05 2016 *)
coxG[{17,595,-34}] (* The coxG program is at A169452 *) (* Harvey P. Dale, Oct 09 2018 *)

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)/(595*t^17 - 34*t^16 - 34*t^15 - 34*t^14 - 34*t^13 - 34*t^12 - 34*t^11 - 34*t^10 - 34*t^9 - 34*t^8 - 34*t^7 - 34*t^6 - 34*t^5 - 34*t^4 - 34*t^3 - 34*t^2 - 34*t + 1).

A168761 Number of reduced words of length n in Coxeter group on 36 generators S_i with relations (S_i)^2 = (S_i S_j)^18 = I.

Original entry on oeis.org

1, 36, 1260, 44100, 1543500, 54022500, 1890787500, 66177562500, 2316214687500, 81067514062500, 2837362992187500, 99307704726562500, 3475769665429687500, 121651938290039062500, 4257817840151367187500, 149023624405297851562500
Offset: 0

Views

Author

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

Keywords

Comments

The initial terms coincide with those of A170755, although the two sequences are eventually different.
First disagreement at index 18: a(18) = 6389387896377145385742186870, A170755(18) = 6389387896377145385742187500. - Klaus Brockhaus, Mar 26 2011
Computed with MAGMA using commands similar to those used to compute A154638.

Links

Crossrefs

Cf. A170755 (G.f.: (1+x)/(1-35*x)).

Programs

  • Mathematica
    coxG[{18,595,-34}] (* The coxG program is at A169452 *) (* Harvey P. Dale, Nov 19 2014 *)
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)/(595*t^18 - 34*t^17 - 34*t^16 - 34*t^15 - 34*t^14 - 34*t^13 - 34*t^12 - 34*t^11 - 34*t^10 - 34*t^9 - 34*t^8 - 34*t^7 - 34*t^6 - 34*t^5 - 34*t^4 - 34*t^3 - 34*t^2 - 34*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)/(595*t^18 - 34*t^17 - 34*t^16 - 34*t^15 - 34*t^14 - 34*t^13 - 34*t^12 - 34*t^11 - 34*t^10 - 34*t^9 - 34*t^8 - 34*t^7 - 34*t^6 - 34*t^5 - 34*t^4 - 34*t^3 - 34*t^2 - 34*t + 1).

A168809 Number of reduced words of length n in Coxeter group on 36 generators S_i with relations (S_i)^2 = (S_i S_j)^19 = I.

Original entry on oeis.org

1, 36, 1260, 44100, 1543500, 54022500, 1890787500, 66177562500, 2316214687500, 81067514062500, 2837362992187500, 99307704726562500, 3475769665429687500, 121651938290039062500, 4257817840151367187500, 149023624405297851562500
Offset: 0

Views

Author

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

Keywords

Comments

The initial terms coincide with those of A170755, although the two sequences are eventually different.
First disagreement at index 19: a(19) = 223628576373200088500976561870, A170755(19) = 223628576373200088500976562500. - Klaus Brockhaus, Apr 01 2011
Computed with MAGMA using commands similar to those used to compute A154638.

Links

Crossrefs

Cf. A170755 (G.f.: (1+x)/(1-35*x)).

Programs

  • Mathematica
    With[{num=Total[2t^Range[18]]+t^19+1,den=Total[-34 t^Range[18]]+ 595t^19+ 1},CoefficientList[Series[num/den,{t,0,20}],t]] (* Harvey P. Dale, Aug 11 2011 *)
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)/(595*t^19 - 34*t^18 - 34*t^17 - 34*t^16 - 34*t^15 - 34*t^14 - 34*t^13 - 34*t^12 - 34*t^11 - 34*t^10 - 34*t^9 - 34*t^8 - 34*t^7 - 34*t^6 - 34*t^5 - 34*t^4 - 34*t^3 - 34*t^2 - 34*t + 1), {t, 0, 50}], t] (* G. C. Greubel, Aug 17 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)/(595*t^19 - 34*t^18 - 34*t^17 - 34*t^16 - 34*t^15 - 34*t^14 - 34*t^13 - 34*t^12 - 34*t^11 - 34*t^10 - 34*t^9 - 34*t^8 - 34*t^7 - 34*t^6 - 34*t^5 - 34*t^4 - 34*t^3 - 34*t^2 - 34*t + 1).

A170717 Number of reduced words of length n in Coxeter group on 36 generators S_i with relations (S_i)^2 = (S_i S_j)^50 = I.

Original entry on oeis.org

1, 36, 1260, 44100, 1543500, 54022500, 1890787500, 66177562500, 2316214687500, 81067514062500, 2837362992187500, 99307704726562500, 3475769665429687500, 121651938290039062500, 4257817840151367187500, 149023624405297851562500
Offset: 0

Views

Author

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

Keywords

Comments

The initial terms coincide with those of A170755, 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 630. - Vincenzo Librandi, Dec 06 2012

Links

Programs

  • Mathematica
    With[{num = Total[2 t^Range[49]]+ t^50 + 1, den = Total[-34  t^Range[49]] + 595 t^50 + 1}, CoefficientList[Series[num/den, {t, 0, 20}], t]] (* Vincenzo Librandi, Dec 06 2012 *)
coxG[{50,595,-34}] (* The coxG program is at A169452 *) (* Harvey P. Dale, Jul 05 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)/(595*t^50 - 34*t^49 - 34*t^48 - 34*t^47 - 34*t^46 - 34*t^45 -
34*t^44 - 34*t^43 - 34*t^42 - 34*t^41 - 34*t^40 - 34*t^39 - 34*t^38 -
34*t^37 - 34*t^36 - 34*t^35 - 34*t^34 - 34*t^33 - 34*t^32 - 34*t^31 -
34*t^30 - 34*t^29 - 34*t^28 - 34*t^27 - 34*t^26 - 34*t^25 - 34*t^24 -
34*t^23 - 34*t^22 - 34*t^21 - 34*t^20 - 34*t^19 - 34*t^18 - 34*t^17 -
34*t^16 - 34*t^15 - 34*t^14 - 34*t^13 - 34*t^12 - 34*t^11 - 34*t^10 -
34*t^9 - 34*t^8 - 34*t^7 - 34*t^6 - 34*t^5 - 34*t^4 - 34*t^3 - 34*t^2 -
34*t + 1).

A162850 Number of reduced words of length n in Coxeter group on 36 generators S_i with relations (S_i)^2 = (S_i S_j)^3 = I.

Original entry on oeis.org

1, 36, 1260, 43470, 1499400, 51707880, 1783182870, 61494142500, 2120662873980, 73132344752670, 2522013244518600, 86973155625205080, 2999321996442766470, 103433437289822465700, 3566964788136020871180, 123008943076595227404270
Offset: 0

Views

Author

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

Keywords

Comments

The initial terms coincide with those of A170755, 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)/(595*t^3 - 34*t^2 - 34*t + 1)

A164672 Number of reduced words of length n in Coxeter group on 36 generators S_i with relations (S_i)^2 = (S_i S_j)^7 = I.

Original entry on oeis.org

1, 36, 1260, 44100, 1543500, 54022500, 1890787500, 66177561870, 2316214643400, 81067511747880, 2837362884186600, 99307700001909000, 3475769467005045000, 121651930188014625000, 4257817516079844021270, 149023611645271179358500
Offset: 0

Views

Author

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

Keywords

Comments

The initial terms coincide with those of A170755, although the two sequences are eventually different.
Computed with MAGMA using commands similar to those used to compute A154638.

Links

Formula

G.f.: (t^7 + 2*t^6 + 2*t^5 + 2*t^4 + 2*t^3 + 2*t^2 + 2*t + 1)/(595*t^7 - 34*t^6 - 34*t^5 - 34*t^4 - 34*t^3 - 34*t^2 - 34*t + 1).

A165168 Number of reduced words of length n in Coxeter group on 36 generators S_i with relations (S_i)^2 = (S_i S_j)^8 = I.

Original entry on oeis.org

1, 36, 1260, 44100, 1543500, 54022500, 1890787500, 66177562500, 2316214686870, 81067514018400, 2837362989872880, 99307704618561600, 3475769660705034000, 121651938091614420000, 4257817832049342750000, 149023624081226328000000
Offset: 0

Views

Author

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

Keywords

Comments

The initial terms coincide with those of A170755, 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)/(595*t^8 -
34*t^7 - 34*t^6 - 34*t^5 - 34*t^4 - 34*t^3 - 34*t^2 - 34*t + 1)

A165651 Number of reduced words of length n in Coxeter group on 36 generators S_i with relations (S_i)^2 = (S_i S_j)^9 = I.

Original entry on oeis.org

1, 36, 1260, 44100, 1543500, 54022500, 1890787500, 66177562500, 2316214687500, 81067514061870, 2837362992143400, 99307704724247880, 3475769665321686600, 121651938285314409000, 4257817839952942545000, 149023624397195827125000
Offset: 0

Views

Author

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

Keywords

Comments

The initial terms coincide with those of A170755, 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^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)/(595*t^9 - 34*t^8 - 34*t^7 - 34*t^6 - 34*t^5 - 34*t^4 - 34*t^3 -
34*t^2 - 34*t + 1)

A168857 Number of reduced words of length n in Coxeter group on 36 generators S_i with relations (S_i)^2 = (S_i S_j)^20 = I.

Original entry on oeis.org

1, 36, 1260, 44100, 1543500, 54022500, 1890787500, 66177562500, 2316214687500, 81067514062500, 2837362992187500, 99307704726562500, 3475769665429687500, 121651938290039062500, 4257817840151367187500, 149023624405297851562500
Offset: 0

Views

Author

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

Keywords

Comments

The initial terms coincide with those of A170755, although the two sequences are eventually different.
First disagreement at index 20: a(20) = 7827000173062003097534179686870, A170755(20) = 7827000173062003097534179687500. - Klaus Brockhaus, Apr 04 2011
Computed with MAGMA using commands similar to those used to compute A154638.

Links

Crossrefs

Cf. A170755 (G.f.: (1+x)/(1-35*x)).

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)/(595*t^20 - 34*t^19 - 34*t^18 - 34*t^17 - 34*t^16 - 34*t^15 - 34*t^14 - 34*t^13 - 34*t^12 - 34*t^11 - 34*t^10 - 34*t^9 - 34*t^8 - 34*t^7 - 34*t^6 - 34*t^5 - 34*t^4 - 34*t^3 - 34*t^2 - 34*t + 1).
Previous Showing 11-20 of 49 results. Next

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