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.

Previous Showing 41-49 of 49 results.

A170276 Number of reduced words of length n in Coxeter group on 27 generators S_i with relations (S_i)^2 = (S_i S_j)^41 = I.

Original entry on oeis.org

1, 27, 702, 18252, 474552, 12338352, 320797152, 8340725952, 216858874752, 5638330743552, 146596599332352, 3811511582641152, 99099301148669952, 2576581829865418752, 66991127576500887552, 1741769316989023076352
Offset: 0

Views

Author

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

Keywords

Comments

The initial terms coincide with those of A170746, although the two sequences are eventually different.
Computed with MAGMA using commands similar to those used to compute A154638.

Programs

Formula

G.f. (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)/(325*t^41 - 25*t^40 - 25*t^39 - 25*t^38 - 25*t^37 - 25*t^36 - 25*t^35
- 25*t^34 - 25*t^33 - 25*t^32 - 25*t^31 - 25*t^30 - 25*t^29 - 25*t^28 -
25*t^27 - 25*t^26 - 25*t^25 - 25*t^24 - 25*t^23 - 25*t^22 - 25*t^21 -
25*t^20 - 25*t^19 - 25*t^18 - 25*t^17 - 25*t^16 - 25*t^15 - 25*t^14 -
25*t^13 - 25*t^12 - 25*t^11 - 25*t^10 - 25*t^9 - 25*t^8 - 25*t^7 -
25*t^6 - 25*t^5 - 25*t^4 - 25*t^3 - 25*t^2 - 25*t + 1)

A170324 Number of reduced words of length n in Coxeter group on 27 generators S_i with relations (S_i)^2 = (S_i S_j)^42 = I.

Original entry on oeis.org

1, 27, 702, 18252, 474552, 12338352, 320797152, 8340725952, 216858874752, 5638330743552, 146596599332352, 3811511582641152, 99099301148669952, 2576581829865418752, 66991127576500887552, 1741769316989023076352
Offset: 0

Views

Author

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

Keywords

Comments

The initial terms coincide with those of A170746, although the two sequences are eventually different.
Computed with MAGMA using commands similar to those used to compute A154638.

Formula

G.f. (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)/(325*t^42 - 25*t^41 - 25*t^40 - 25*t^39 - 25*t^38 - 25*t^37 -
25*t^36 - 25*t^35 - 25*t^34 - 25*t^33 - 25*t^32 - 25*t^31 - 25*t^30 -
25*t^29 - 25*t^28 - 25*t^27 - 25*t^26 - 25*t^25 - 25*t^24 - 25*t^23 -
25*t^22 - 25*t^21 - 25*t^20 - 25*t^19 - 25*t^18 - 25*t^17 - 25*t^16 -
25*t^15 - 25*t^14 - 25*t^13 - 25*t^12 - 25*t^11 - 25*t^10 - 25*t^9 -
25*t^8 - 25*t^7 - 25*t^6 - 25*t^5 - 25*t^4 - 25*t^3 - 25*t^2 - 25*t + 1)

A170372 Number of reduced words of length n in Coxeter group on 27 generators S_i with relations (S_i)^2 = (S_i S_j)^43 = I.

Original entry on oeis.org

1, 27, 702, 18252, 474552, 12338352, 320797152, 8340725952, 216858874752, 5638330743552, 146596599332352, 3811511582641152, 99099301148669952, 2576581829865418752, 66991127576500887552, 1741769316989023076352
Offset: 0

Views

Author

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

Keywords

Comments

The initial terms coincide with those of A170746, although the two sequences are eventually different.
Computed with MAGMA using commands similar to those used to compute A154638.

Formula

G.f. (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)/(325*t^43 - 25*t^42 - 25*t^41 - 25*t^40 - 25*t^39 -
25*t^38 - 25*t^37 - 25*t^36 - 25*t^35 - 25*t^34 - 25*t^33 - 25*t^32 -
25*t^31 - 25*t^30 - 25*t^29 - 25*t^28 - 25*t^27 - 25*t^26 - 25*t^25 -
25*t^24 - 25*t^23 - 25*t^22 - 25*t^21 - 25*t^20 - 25*t^19 - 25*t^18 -
25*t^17 - 25*t^16 - 25*t^15 - 25*t^14 - 25*t^13 - 25*t^12 - 25*t^11 -
25*t^10 - 25*t^9 - 25*t^8 - 25*t^7 - 25*t^6 - 25*t^5 - 25*t^4 - 25*t^3 -
25*t^2 - 25*t + 1)

A170420 Number of reduced words of length n in Coxeter group on 27 generators S_i with relations (S_i)^2 = (S_i S_j)^44 = I.

Original entry on oeis.org

1, 27, 702, 18252, 474552, 12338352, 320797152, 8340725952, 216858874752, 5638330743552, 146596599332352, 3811511582641152, 99099301148669952, 2576581829865418752, 66991127576500887552, 1741769316989023076352
Offset: 0

Views

Author

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

Keywords

Comments

The initial terms coincide with those of A170746, although the two sequences are eventually different.
Computed with MAGMA using commands similar to those used to compute A154638.

Formula

G.f. (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)/(325*t^44 - 25*t^43 - 25*t^42 - 25*t^41 -
25*t^40 - 25*t^39 - 25*t^38 - 25*t^37 - 25*t^36 - 25*t^35 - 25*t^34 -
25*t^33 - 25*t^32 - 25*t^31 - 25*t^30 - 25*t^29 - 25*t^28 - 25*t^27 -
25*t^26 - 25*t^25 - 25*t^24 - 25*t^23 - 25*t^22 - 25*t^21 - 25*t^20 -
25*t^19 - 25*t^18 - 25*t^17 - 25*t^16 - 25*t^15 - 25*t^14 - 25*t^13 -
25*t^12 - 25*t^11 - 25*t^10 - 25*t^9 - 25*t^8 - 25*t^7 - 25*t^6 - 25*t^5
- 25*t^4 - 25*t^3 - 25*t^2 - 25*t + 1)

A170468 Number of reduced words of length n in Coxeter group on 27 generators S_i with relations (S_i)^2 = (S_i S_j)^45 = I.

Original entry on oeis.org

1, 27, 702, 18252, 474552, 12338352, 320797152, 8340725952, 216858874752, 5638330743552, 146596599332352, 3811511582641152, 99099301148669952, 2576581829865418752, 66991127576500887552, 1741769316989023076352
Offset: 0

Views

Author

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

Keywords

Comments

The initial terms coincide with those of A170746, although the two sequences are eventually different.
Computed with MAGMA using commands similar to those used to compute A154638.

Programs

  • Mathematica
    With[{num=Total[2t^Range[44]]+t^45+1,den=Total[-25 t^Range[44]]+ 325t^45+ 1},CoefficientList[Series[num/den,{t,0,20}],t]] (* Harvey P. Dale, Dec 05 2012 *)

Formula

G.f. (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)/(325*t^45 - 25*t^44 - 25*t^43 -
25*t^42 - 25*t^41 - 25*t^40 - 25*t^39 - 25*t^38 - 25*t^37 - 25*t^36 -
25*t^35 - 25*t^34 - 25*t^33 - 25*t^32 - 25*t^31 - 25*t^30 - 25*t^29 -
25*t^28 - 25*t^27 - 25*t^26 - 25*t^25 - 25*t^24 - 25*t^23 - 25*t^22 -
25*t^21 - 25*t^20 - 25*t^19 - 25*t^18 - 25*t^17 - 25*t^16 - 25*t^15 -
25*t^14 - 25*t^13 - 25*t^12 - 25*t^11 - 25*t^10 - 25*t^9 - 25*t^8 -
25*t^7 - 25*t^6 - 25*t^5 - 25*t^4 - 25*t^3 - 25*t^2 - 25*t + 1)

A170516 Number of reduced words of length n in Coxeter group on 27 generators S_i with relations (S_i)^2 = (S_i S_j)^46 = I.

Original entry on oeis.org

1, 27, 702, 18252, 474552, 12338352, 320797152, 8340725952, 216858874752, 5638330743552, 146596599332352, 3811511582641152, 99099301148669952, 2576581829865418752, 66991127576500887552, 1741769316989023076352
Offset: 0

Views

Author

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

Keywords

Comments

The initial terms coincide with those of A170746, although the two sequences are eventually different.
Computed with MAGMA using commands similar to those used to compute A154638.

Programs

Formula

G.f. (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)/(325*t^46 - 25*t^45 -
25*t^44 - 25*t^43 - 25*t^42 - 25*t^41 - 25*t^40 - 25*t^39 - 25*t^38 -
25*t^37 - 25*t^36 - 25*t^35 - 25*t^34 - 25*t^33 - 25*t^32 - 25*t^31 -
25*t^30 - 25*t^29 - 25*t^28 - 25*t^27 - 25*t^26 - 25*t^25 - 25*t^24 -
25*t^23 - 25*t^22 - 25*t^21 - 25*t^20 - 25*t^19 - 25*t^18 - 25*t^17 -
25*t^16 - 25*t^15 - 25*t^14 - 25*t^13 - 25*t^12 - 25*t^11 - 25*t^10 -
25*t^9 - 25*t^8 - 25*t^7 - 25*t^6 - 25*t^5 - 25*t^4 - 25*t^3 - 25*t^2 -
25*t + 1)

A170564 Number of reduced words of length n in Coxeter group on 27 generators S_i with relations (S_i)^2 = (S_i S_j)^47 = I.

Original entry on oeis.org

1, 27, 702, 18252, 474552, 12338352, 320797152, 8340725952, 216858874752, 5638330743552, 146596599332352, 3811511582641152, 99099301148669952, 2576581829865418752, 66991127576500887552, 1741769316989023076352
Offset: 0

Views

Author

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

Keywords

Comments

The initial terms coincide with those of A170746, although the two sequences are eventually different.
Computed with MAGMA using commands similar to those used to compute A154638.

Programs

Formula

G.f. (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)/(325*t^47 -
25*t^46 - 25*t^45 - 25*t^44 - 25*t^43 - 25*t^42 - 25*t^41 - 25*t^40 -
25*t^39 - 25*t^38 - 25*t^37 - 25*t^36 - 25*t^35 - 25*t^34 - 25*t^33 -
25*t^32 - 25*t^31 - 25*t^30 - 25*t^29 - 25*t^28 - 25*t^27 - 25*t^26 -
25*t^25 - 25*t^24 - 25*t^23 - 25*t^22 - 25*t^21 - 25*t^20 - 25*t^19 -
25*t^18 - 25*t^17 - 25*t^16 - 25*t^15 - 25*t^14 - 25*t^13 - 25*t^12 -
25*t^11 - 25*t^10 - 25*t^9 - 25*t^8 - 25*t^7 - 25*t^6 - 25*t^5 - 25*t^4
- 25*t^3 - 25*t^2 - 25*t + 1)

A170612 Number of reduced words of length n in Coxeter group on 27 generators S_i with relations (S_i)^2 = (S_i S_j)^48 = I.

Original entry on oeis.org

1, 27, 702, 18252, 474552, 12338352, 320797152, 8340725952, 216858874752, 5638330743552, 146596599332352, 3811511582641152, 99099301148669952, 2576581829865418752, 66991127576500887552, 1741769316989023076352
Offset: 0

Views

Author

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

Keywords

Comments

The initial terms coincide with those of A170746, although the two sequences are eventually different.
Computed with MAGMA using commands similar to those used to compute A154638.

Formula

G.f. (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)/(325*t^48 - 25*t^47 - 25*t^46 - 25*t^45 - 25*t^44 - 25*t^43 - 25*t^42
- 25*t^41 - 25*t^40 - 25*t^39 - 25*t^38 - 25*t^37 - 25*t^36 - 25*t^35 -
25*t^34 - 25*t^33 - 25*t^32 - 25*t^31 - 25*t^30 - 25*t^29 - 25*t^28 -
25*t^27 - 25*t^26 - 25*t^25 - 25*t^24 - 25*t^23 - 25*t^22 - 25*t^21 -
25*t^20 - 25*t^19 - 25*t^18 - 25*t^17 - 25*t^16 - 25*t^15 - 25*t^14 -
25*t^13 - 25*t^12 - 25*t^11 - 25*t^10 - 25*t^9 - 25*t^8 - 25*t^7 -
25*t^6 - 25*t^5 - 25*t^4 - 25*t^3 - 25*t^2 - 25*t + 1)

A170660 Number of reduced words of length n in Coxeter group on 27 generators S_i with relations (S_i)^2 = (S_i S_j)^49 = I.

Original entry on oeis.org

1, 27, 702, 18252, 474552, 12338352, 320797152, 8340725952, 216858874752, 5638330743552, 146596599332352, 3811511582641152, 99099301148669952, 2576581829865418752, 66991127576500887552, 1741769316989023076352
Offset: 0

Views

Author

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

Keywords

Comments

The initial terms coincide with those of A170746, although the two sequences are eventually different.
Computed with MAGMA using commands similar to those used to compute A154638.

Programs

Formula

G.f. (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)/(325*t^49 - 25*t^48 - 25*t^47 - 25*t^46 - 25*t^45 - 25*t^44 - 25*t^43
- 25*t^42 - 25*t^41 - 25*t^40 - 25*t^39 - 25*t^38 - 25*t^37 - 25*t^36 -
25*t^35 - 25*t^34 - 25*t^33 - 25*t^32 - 25*t^31 - 25*t^30 - 25*t^29 -
25*t^28 - 25*t^27 - 25*t^26 - 25*t^25 - 25*t^24 - 25*t^23 - 25*t^22 -
25*t^21 - 25*t^20 - 25*t^19 - 25*t^18 - 25*t^17 - 25*t^16 - 25*t^15 -
25*t^14 - 25*t^13 - 25*t^12 - 25*t^11 - 25*t^10 - 25*t^9 - 25*t^8 -
25*t^7 - 25*t^6 - 25*t^5 - 25*t^4 - 25*t^3 - 25*t^2 - 25*t + 1)
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