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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A170265 Number of reduced words of length n in Coxeter group on 16 generators S_i with relations (S_i)^2 = (S_i S_j)^41 = 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

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)/(105*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)

A170313 Number of reduced words of length n in Coxeter group on 16 generators S_i with relations (S_i)^2 = (S_i S_j)^42 = 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

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)/(105*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)

A170361 Number of reduced words of length n in Coxeter group on 16 generators S_i with relations (S_i)^2 = (S_i S_j)^43 = 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[42]]+t^43+1,den=Total[-14 t^Range[42]]+105t^43+ 1},CoefficientList[Series[num/den,{t,0,30}],t]] (* Harvey P. Dale, Oct 14 2013 *)

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)/(105*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)

A170409 Number of reduced words of length n in Coxeter group on 16 generators S_i with relations (S_i)^2 = (S_i S_j)^44 = 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
    coxG[{44,105,-14}] (* See A169452 for the coxG program *) (* Harvey P. Dale, Aug 31 2014 *)

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)/(105*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)

A170457 Number of reduced words of length n in Coxeter group on 16 generators S_i with relations (S_i)^2 = (S_i S_j)^45 = 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

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)/(105*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)

A170505 Number of reduced words of length n in Coxeter group on 16 generators S_i with relations (S_i)^2 = (S_i S_j)^46 = 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

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)/(105*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)

A170553 Number of reduced words of length n in Coxeter group on 16 generators S_i with relations (S_i)^2 = (S_i S_j)^47 = 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

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)/(105*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)

A170601 Number of reduced words of length n in Coxeter group on 16 generators S_i with relations (S_i)^2 = (S_i S_j)^48 = 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

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)/(105*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)

A170649 Number of reduced words of length n in Coxeter group on 16 generators S_i with relations (S_i)^2 = (S_i S_j)^49 = 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

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)/(105*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).
a(n) = -105*a(n-49) + 14*Sum_{k=1..48} a(n-k). - Wesley Ivan Hurt, May 04 2024
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