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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A168693 Number of reduced words of length n in Coxeter group on 16 generators S_i with relations (S_i)^2 = (S_i S_j)^17 = I.

Original entry on oeis.org

1, 16, 240, 3600, 54000, 810000, 12150000, 182250000, 2733750000, 41006250000, 615093750000, 9226406250000, 138396093750000, 2075941406250000, 31139121093750000, 467086816406250000, 7006302246093750000
Offset: 0

Views

Author

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

Keywords

Comments

The initial terms coincide with those of A170735, although the two sequences are eventually different.
First disagreement at index 17: a(17) = 105094533691406249880, A170735(17) = 105094533691406250000. - Klaus Brockhaus, Mar 30 2011
Computed with MAGMA using commands similar to those used to compute A154638.

Links

Crossrefs

Cf. A170735 (G.f.: (1+x)/(1-15*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)/(105*t^17 - 14*t^16 - 14*t^15 - 14*t^14 - 14*t^13 - 14*t^12 - 14*t^11 - 14*t^10 - 14*t^9 - 14*t^8 - 14*t^7 - 14*t^6 - 14*t^5 - 14*t^4 - 14*t^3 - 14*t^2 - 14*t + 1), {t,0,50}], t] (* G. C. Greubel, Aug 03 2016 *)
coxG[{17,105,-14}] (* The coxG program is at A169452 *) (* Harvey P. Dale, Jul 05 2017 *)

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)/ (105*t^17 - 14*t^16 - 14*t^15 - 14*t^14 - 14*t^13 - 14*t^12 - 14*t^11 - 14*t^10 - 14*t^9 - 14*t^8 - 14*t^7 - 14*t^6 - 14*t^5 - 14*t^4 - 14*t^3 - 14*t^2 - 14*t + 1).

A168741 Number of reduced words of length n in Coxeter group on 16 generators S_i with relations (S_i)^2 = (S_i S_j)^18 = I.

Original entry on oeis.org

1, 16, 240, 3600, 54000, 810000, 12150000, 182250000, 2733750000, 41006250000, 615093750000, 9226406250000, 138396093750000, 2075941406250000, 31139121093750000, 467086816406250000, 7006302246093750000
Offset: 0

Views

Author

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

Keywords

Comments

The initial terms coincide with those of A170735, although the two sequences are eventually different.
First disagreement at index 18: a(18) = 1576418005371093749880, A170735(18) = 1576418005371093750000. - Klaus Brockhaus, Mar 27 2011
Computed with MAGMA using commands similar to those used to compute A154638.

Links

Crossrefs

Cf. A170735 (G.f.: (1+x)/(1-15*x)).

Programs

  • Mathematica
    With[{num=Total[2t^Range[17]]+t^18+1,den=Total[-14 t^Range[17]]+ 105t^18+ 1}, CoefficientList[Series[num/den,{t,0,30}],t]] (* Harvey P. Dale, Oct 04 2011 *)
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)/(105*t^18 - 14*t^17 - 14*t^16 - 14*t^15 - 14*t^14 - 14*t^13 - 14*t^12 - 14*t^11 - 14*t^10 - 14*t^9 - 14*t^8 - 14*t^7 - 14*t^6 - 14*t^5 - 14*t^4 - 14*t^3 - 14*t^2 - 14*t + 1), {t, 0, 50}], t] (* G. C. Greubel, Aug 10 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)/(105*t^18 - 14*t^17 - 14*t^16 - 14*t^15 - 14*t^14 - 14*t^13 - 14*t^12 - 14*t^11 - 14*t^10 - 14*t^9 - 14*t^8 - 14*t^7 - 14*t^6 - 14*t^5 - 14*t^4 - 14*t^3 - 14*t^2 - 14*t + 1).

A168789 Number of reduced words of length n in Coxeter group on 16 generators S_i with relations (S_i)^2 = (S_i S_j)^19 = I.

Original entry on oeis.org

1, 16, 240, 3600, 54000, 810000, 12150000, 182250000, 2733750000, 41006250000, 615093750000, 9226406250000, 138396093750000, 2075941406250000, 31139121093750000, 467086816406250000, 7006302246093750000
Offset: 0

Views

Author

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

Keywords

Comments

The initial terms coincide with those of A170735, although the two sequences are eventually different.
First disagreement at index 19: a(19) = 23646270080566406249880, A170735(19) = 23646270080566406250000. - Klaus Brockhaus, Mar 30 2011
Computed with MAGMA using commands similar to those used to compute A154638.

Links

Crossrefs

Cf. A170735 (G.f.: (1+x)/(1-15*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)/(105*t^19 - 14*t^18 - 14*t^17 - 14*t^16 - 14*t^15 - 14*t^14 - 14*t^13 - 14*t^12 - 14*t^11 - 14*t^10 - 14*t^9 - 14*t^8 - 14*t^7 - 14*t^6 - 14*t^5 - 14*t^4 - 14*t^3 - 14*t^2 - 14*t + 1), {t, 0, 50}], t] (* G. C. Greubel, Aug 15 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)/(105*t^19 - 14*t^18 - 14*t^17 - 14*t^16 - 14*t^15 - 14*t^14 - 14*t^13 - 14*t^12 - 14*t^11 - 14*t^10 - 14*t^9 - 14*t^8 - 14*t^7 - 14*t^6 - 14*t^5 - 14*t^4 - 14*t^3 - 14*t^2 - 14*t + 1).

A169557 Number of reduced words of length n in Coxeter group on 16 generators S_i with relations (S_i)^2 = (S_i S_j)^35 = I.

Original entry on oeis.org

1, 16, 240, 3600, 54000, 810000, 12150000, 182250000, 2733750000, 41006250000, 615093750000, 9226406250000, 138396093750000, 2075941406250000, 31139121093750000, 467086816406250000, 7006302246093750000
Offset: 0

Views

Author

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

Keywords

Comments

The initial terms coincide with those of A170735, 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[34]]+t^35+1,den=Total[-14 t^Range[34]]+105t^35+ 1},CoefficientList[Series[num/den,{t,0,30}],t]] (* Harvey P. Dale, Feb 25 2014 *)

Formula

G.f. (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)/(105*t^35 - 14*t^34 - 14*t^33 - 14*t^32 - 14*t^31 -
14*t^30 - 14*t^29 - 14*t^28 - 14*t^27 - 14*t^26 - 14*t^25 - 14*t^24 -
14*t^23 - 14*t^22 - 14*t^21 - 14*t^20 - 14*t^19 - 14*t^18 - 14*t^17 -
14*t^16 - 14*t^15 - 14*t^14 - 14*t^13 - 14*t^12 - 14*t^11 - 14*t^10 -
14*t^9 - 14*t^8 - 14*t^7 - 14*t^6 - 14*t^5 - 14*t^4 - 14*t^3 - 14*t^2 -
14*t + 1)

A170697 Number of reduced words of length n in Coxeter group on 16 generators S_i with relations (S_i)^2 = (S_i S_j)^50 = I.

Original entry on oeis.org

1, 16, 240, 3600, 54000, 810000, 12150000, 182250000, 2733750000, 41006250000, 615093750000, 9226406250000, 138396093750000, 2075941406250000, 31139121093750000, 467086816406250000, 7006302246093750000
Offset: 0

Views

Author

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

Keywords

Comments

The initial terms coincide with those of A170735, 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 120. - Vincenzo Librandi, Dec 08 2012

Links

Programs

  • Mathematica
    With[{num = Total[2 t^Range[49]] + t^50 + 1, den = Total[-14 t^Range[49]] + 105t^50 + 1}, CoefficientList[Series[num/den, {t, 0, 20}], t]] (* Vincenzo Librandi, Dec 08 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)/(105*t^50 - 14*t^49 - 14*t^48 - 14*t^47 - 14*t^46 - 14*t^45 -
14*t^44 - 14*t^43 - 14*t^42 - 14*t^41 - 14*t^40 - 14*t^39 - 14*t^38 -
14*t^37 - 14*t^36 - 14*t^35 - 14*t^34 - 14*t^33 - 14*t^32 - 14*t^31 -
14*t^30 - 14*t^29 - 14*t^28 - 14*t^27 - 14*t^26 - 14*t^25 - 14*t^24 -
14*t^23 - 14*t^22 - 14*t^21 - 14*t^20 - 14*t^19 - 14*t^18 - 14*t^17 -
14*t^16 - 14*t^15 - 14*t^14 - 14*t^13 - 14*t^12 - 14*t^11 - 14*t^10 -
14*t^9 - 14*t^8 - 14*t^7 - 14*t^6 - 14*t^5 - 14*t^4 - 14*t^3 - 14*t^2 -
14*t + 1).

A162791 Number of reduced words of length n in Coxeter group on 16 generators S_i with relations (S_i)^2 = (S_i S_j)^3 = I.

Original entry on oeis.org

1, 16, 240, 3480, 50400, 729120, 10547880, 152586000, 2207316720, 31931110680, 461916453600, 6682097644320, 96663430749480, 1398336169885200, 20228374156231920, 292624284336944280, 4233111921066520800
Offset: 0

Views

Author

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

Keywords

Comments

The initial terms coincide with those of A170735, 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^3+2t^2+2t+1)/(105t^3-14t^2-14t+1), {t,0,30}],t] (* Harvey P. Dale, Oct 02 2011 *)

Formula

G.f.: (t^3 + 2*t^2 + 2*t + 1)/(105*t^3 - 14*t^2 - 14*t + 1)

A163092 Number of reduced words of length n in Coxeter group on 16 generators S_i with relations (S_i)^2 = (S_i S_j)^4 = I.

Original entry on oeis.org

1, 16, 240, 3600, 53880, 806400, 12069120, 180633600, 2703470280, 40461750000, 605574696720, 9063392310000, 135648138214680, 2030190989349600, 30385049935084320, 454760790684530400, 6806221388012959080, 101865971146974325200, 1524586916316221551920
Offset: 0

Views

Author

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

Keywords

Comments

The initial terms coincide with those of A170735, 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^4 + 2*t^3 + 2*t^2 + 2*t + 1)/(105*t^4 - 14*t^3 - 14*t^2 - 14*t + 1), {t, 0, 16}], t] (* Jean-François Alcover, Nov 26 2013 *)
  • PARI
    Vec((t^4 + 2*t^3 + 2*t^2 + 2*t + 1)/(105*t^4 - 14*t^3 - 14*t^2 - 14*t + 1) + O(t^20)) \\ Jinyuan Wang, Mar 23 2020

Formula

G.f.: (t^4 + 2*t^3 + 2*t^2 + 2*t + 1)/(105*t^4 - 14*t^3 - 14*t^2 - 14*t + 1).

Extensions

More terms from Jinyuan Wang, Mar 23 2020

A164627 Number of reduced words of length n in Coxeter group on 16 generators S_i with relations (S_i)^2 = (S_i S_j)^7 = I.

Original entry on oeis.org

1, 16, 240, 3600, 54000, 810000, 12150000, 182249880, 2733746400, 41006169120, 615092133600, 9226375956000, 138395548620000, 2075931868500000, 31138957615514280, 467084058053130000, 7006256278106196720
Offset: 0

Views

Author

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

Keywords

Comments

The initial terms coincide with those of A170735, 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)/(105*t^7 - 14*t^6 - 14*t^5 - 14*t^4 - 14*t^3 - 14*t^2 - 14*t + 1).

A164867 Number of reduced words of length n in Coxeter group on 16 generators S_i with relations (S_i)^2 = (S_i S_j)^8 = I.

Original entry on oeis.org

1, 16, 240, 3600, 54000, 810000, 12150000, 182250000, 2733749880, 41006246400, 615093669120, 9226404633600, 138396063456000, 2075940861120000, 31139111556000000, 467086652928000000, 7006299487740014280
Offset: 0

Views

Author

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

Keywords

Comments

The initial terms coincide with those of A170735, 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)/(105*t^8 -
14*t^7 - 14*t^6 - 14*t^5 - 14*t^4 - 14*t^3 - 14*t^2 - 14*t + 1)

A165308 Number of reduced words of length n in Coxeter group on 16 generators S_i with relations (S_i)^2 = (S_i S_j)^9 = I.

Original entry on oeis.org

1, 16, 240, 3600, 54000, 810000, 12150000, 182250000, 2733750000, 41006249880, 615093746400, 9226406169120, 138396092133600, 2075941375956000, 31139120548620000, 467086806868500000, 7006302082615500000
Offset: 0

Views

Author

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

Keywords

Comments

The initial terms coincide with those of A170735, 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)/(105*t^9 - 14*t^8 - 14*t^7 - 14*t^6 - 14*t^5 - 14*t^4 - 14*t^3 -
14*t^2 - 14*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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