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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A169283 Number of reduced words of length n in Coxeter group on 30 generators S_i with relations (S_i)^2 = (S_i S_j)^29 = I.

Original entry on oeis.org

1, 30, 870, 25230, 731670, 21218430, 615334470, 17844699630, 517496289270, 15007392388830, 435214379276070, 12621216999006030, 366015292971174870, 10614443496164071230, 307818861388758065670, 8926746980273983904430
Offset: 0

Views

Author

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

Keywords

Comments

The initial terms coincide with those of A170749, although the two sequences are eventually different.
First disagreement at index 29: a(29) = 2656227054994356346098442980756223579120395, A170749(29) = 2656227054994356346098442980756223579120830. - Klaus Brockhaus, Jun 03 2011
Computed with Magma using commands similar to those used to compute A154638.

Crossrefs

Cf. A170749 (G.f.: (1+x)/(1-29*x)).

Programs

  • Mathematica
    With[{num=Total[2t^Range[28]]+1+t^29,den=Total[-28 t^Range[28]]+ 1+ 406t^29}, CoefficientList[Series[num/den,{t,0,20}],t]] (* Harvey P. Dale, Jun 15 2011 *)

Formula

G.f.: (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)/(406*t^29 - 28*t^28 - 28*t^27 - 28*t^26 - 28*t^25 - 28*t^24 - 28*t^23 - 28*t^22 - 28*t^21 - 28*t^20 - 28*t^19 - 28*t^18 - 28*t^17 - 28*t^16 - 28*t^15 - 28*t^14 - 28*t^13 - 28*t^12 - 28*t^11 - 28*t^10 - 28*t^9 - 28*t^8 - 28*t^7 - 28*t^6 - 28*t^5 - 28*t^4 - 28*t^3 - 28*t^2 - 28*t + 1).

A169331 Number of reduced words of length n in Coxeter group on 30 generators S_i with relations (S_i)^2 = (S_i S_j)^30 = I.

Original entry on oeis.org

1, 30, 870, 25230, 731670, 21218430, 615334470, 17844699630, 517496289270, 15007392388830, 435214379276070, 12621216999006030, 366015292971174870, 10614443496164071230, 307818861388758065670, 8926746980273983904430
Offset: 0

Views

Author

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

Keywords

Comments

The initial terms coincide with those of A170749, although the two sequences are eventually different.
First disagreement at index 30: a(30) = 77030584594836334036854846441930483794503635, A170749(30) = 77030584594836334036854846441930483794504070. - Klaus Brockhaus, Jun 23 2011
Computed with Magma using commands similar to those used to compute A154638.

Crossrefs

Cf. A170749 (G.f.: (1+x)/(1-29*x)).

Programs

Formula

G.f.: (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)/(406*t^30 - 28*t^29 - 28*t^28 - 28*t^27 - 28*t^26 - 28*t^25 - 28*t^24 - 28*t^23 - 28*t^22 - 28*t^21 - 28*t^20 - 28*t^19 - 28*t^18 - 28*t^17 - 28*t^16 - 28*t^15 - 28*t^14 - 28*t^13 - 28*t^12 - 28*t^11 - 28*t^10 - 28*t^9 - 28*t^8 - 28*t^7 - 28*t^6 - 28*t^5 - 28*t^4 - 28*t^3 - 28*t^2 - 28*t + 1).

A169379 Number of reduced words of length n in Coxeter group on 30 generators S_i with relations (S_i)^2 = (S_i S_j)^31 = I.

Original entry on oeis.org

1, 30, 870, 25230, 731670, 21218430, 615334470, 17844699630, 517496289270, 15007392388830, 435214379276070, 12621216999006030, 366015292971174870, 10614443496164071230, 307818861388758065670, 8926746980273983904430
Offset: 0

Views

Author

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

Keywords

Comments

The initial terms coincide with those of A170749, although the two sequences are eventually different.
First disagreement at index 31: a(31) = 2233886953250253687068790546815984030040617595, A170749(31) = 2233886953250253687068790546815984030040618030. - Klaus Brockhaus, Jun 17 2011
Computed with Magma using commands similar to those used to compute A154638.

Crossrefs

Cf. A170749 (G.f.: (1+x)/(1-29*x)).

Programs

Formula

G.f.: (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)/(406*t^31 - 28*t^30 - 28*t^29 - 28*t^28 - 28*t^27 - 28*t^26 - 28*t^25 - 28*t^24 - 28*t^23 - 28*t^22 - 28*t^21 - 28*t^20 - 28*t^19 - 28*t^18 - 28*t^17 - 28*t^16 - 28*t^15 - 28*t^14 - 28*t^13 - 28*t^12 - 28*t^11 - 28*t^10 - 28*t^9 - 28*t^8 - 28*t^7 - 28*t^6 - 28*t^5 - 28*t^4 - 28*t^3 - 28*t^2 - 28*t + 1).

A169427 Number of reduced words of length n in Coxeter group on 30 generators S_i with relations (S_i)^2 = (S_i S_j)^32 = I.

Original entry on oeis.org

1, 30, 870, 25230, 731670, 21218430, 615334470, 17844699630, 517496289270, 15007392388830, 435214379276070, 12621216999006030, 366015292971174870, 10614443496164071230, 307818861388758065670, 8926746980273983904430
Offset: 0

Views

Author

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

Keywords

Comments

The initial terms coincide with those of A170749, although the two sequences are eventually different.
First disagreement is at index 32, the difference is 435. - Klaus Brockhaus, Jun 27 2011
Computed with Magma using commands similar to those used to compute A154638.

Crossrefs

Cf. A170749 (G.f.: (1+x)/(1-29*x) ).

Formula

G.f.: (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)/(406*t^32 - 28*t^31 - 28*t^30 - 28*t^29 - 28*t^28 - 28*t^27 - 28*t^26 - 28*t^25 - 28*t^24 - 28*t^23 - 28*t^22 - 28*t^21 - 28*t^20 - 28*t^19 - 28*t^18 - 28*t^17 - 28*t^16 - 28*t^15 - 28*t^14 - 28*t^13 - 28*t^12 - 28*t^11 - 28*t^10 - 28*t^9 - 28*t^8 - 28*t^7 - 28*t^6 - 28*t^5 - 28*t^4 - 28*t^3 - 28*t^2 - 28*t + 1).
G.f.: (1+2*sum(k=1..31, x^k)+x^32)/(1-28*sum(k=1..31, x^k)+406*x^32).

A169475 Number of reduced words of length n in Coxeter group on 30 generators S_i with relations (S_i)^2 = (S_i S_j)^33 = I.

Original entry on oeis.org

1, 30, 870, 25230, 731670, 21218430, 615334470, 17844699630, 517496289270, 15007392388830, 435214379276070, 12621216999006030, 366015292971174870, 10614443496164071230, 307818861388758065670, 8926746980273983904430
Offset: 0

Views

Author

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

Keywords

Comments

The initial terms coincide with those of A170749, although the two sequences are eventually different.
Computed with MAGMA using commands similar to those used to compute A154638.

Formula

G.f. (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)/(406*t^33 - 28*t^32 - 28*t^31 - 28*t^30 - 28*t^29 - 28*t^28 - 28*t^27
- 28*t^26 - 28*t^25 - 28*t^24 - 28*t^23 - 28*t^22 - 28*t^21 - 28*t^20 -
28*t^19 - 28*t^18 - 28*t^17 - 28*t^16 - 28*t^15 - 28*t^14 - 28*t^13 -
28*t^12 - 28*t^11 - 28*t^10 - 28*t^9 - 28*t^8 - 28*t^7 - 28*t^6 - 28*t^5
- 28*t^4 - 28*t^3 - 28*t^2 - 28*t + 1)

A169523 Number of reduced words of length n in Coxeter group on 30 generators S_i with relations (S_i)^2 = (S_i S_j)^34 = I.

Original entry on oeis.org

1, 30, 870, 25230, 731670, 21218430, 615334470, 17844699630, 517496289270, 15007392388830, 435214379276070, 12621216999006030, 366015292971174870, 10614443496164071230, 307818861388758065670, 8926746980273983904430
Offset: 0

Views

Author

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

Keywords

Comments

The initial terms coincide with those of A170749, although the two sequences are eventually different.
Computed with MAGMA using commands similar to those used to compute A154638.

Programs

Formula

G.f. (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)/(406*t^34 - 28*t^33 - 28*t^32 - 28*t^31 - 28*t^30 - 28*t^29 -
28*t^28 - 28*t^27 - 28*t^26 - 28*t^25 - 28*t^24 - 28*t^23 - 28*t^22 -
28*t^21 - 28*t^20 - 28*t^19 - 28*t^18 - 28*t^17 - 28*t^16 - 28*t^15 -
28*t^14 - 28*t^13 - 28*t^12 - 28*t^11 - 28*t^10 - 28*t^9 - 28*t^8 -
28*t^7 - 28*t^6 - 28*t^5 - 28*t^4 - 28*t^3 - 28*t^2 - 28*t + 1)

A169571 Number of reduced words of length n in Coxeter group on 30 generators S_i with relations (S_i)^2 = (S_i S_j)^35 = I.

Original entry on oeis.org

1, 30, 870, 25230, 731670, 21218430, 615334470, 17844699630, 517496289270, 15007392388830, 435214379276070, 12621216999006030, 366015292971174870, 10614443496164071230, 307818861388758065670, 8926746980273983904430
Offset: 0

Views

Author

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

Keywords

Comments

The initial terms coincide with those of A170749, 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[34]]+t^35+1,den=Total[-28 t^Range[34]]+406t^35+ 1},CoefficientList[Series[num/den,{t,0,30}],t]] (* Harvey P. Dale, May 30 2013 *)

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)/(406*t^35 - 28*t^34 - 28*t^33 - 28*t^32 - 28*t^31 -
28*t^30 - 28*t^29 - 28*t^28 - 28*t^27 - 28*t^26 - 28*t^25 - 28*t^24 -
28*t^23 - 28*t^22 - 28*t^21 - 28*t^20 - 28*t^19 - 28*t^18 - 28*t^17 -
28*t^16 - 28*t^15 - 28*t^14 - 28*t^13 - 28*t^12 - 28*t^11 - 28*t^10 -
28*t^9 - 28*t^8 - 28*t^7 - 28*t^6 - 28*t^5 - 28*t^4 - 28*t^3 - 28*t^2 -
28*t + 1)

A170039 Number of reduced words of length n in Coxeter group on 30 generators S_i with relations (S_i)^2 = (S_i S_j)^36 = I.

Original entry on oeis.org

1, 30, 870, 25230, 731670, 21218430, 615334470, 17844699630, 517496289270, 15007392388830, 435214379276070, 12621216999006030, 366015292971174870, 10614443496164071230, 307818861388758065670, 8926746980273983904430
Offset: 0

Views

Author

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

Keywords

Comments

The initial terms coincide with those of A170749, although the two sequences are eventually different.
Computed with MAGMA using commands similar to those used to compute A154638.

Programs

Formula

G.f. (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)/(406*t^36 - 28*t^35 - 28*t^34 - 28*t^33 -
28*t^32 - 28*t^31 - 28*t^30 - 28*t^29 - 28*t^28 - 28*t^27 - 28*t^26 -
28*t^25 - 28*t^24 - 28*t^23 - 28*t^22 - 28*t^21 - 28*t^20 - 28*t^19 -
28*t^18 - 28*t^17 - 28*t^16 - 28*t^15 - 28*t^14 - 28*t^13 - 28*t^12 -
28*t^11 - 28*t^10 - 28*t^9 - 28*t^8 - 28*t^7 - 28*t^6 - 28*t^5 - 28*t^4
- 28*t^3 - 28*t^2 - 28*t + 1)

A170087 Number of reduced words of length n in Coxeter group on 30 generators S_i with relations (S_i)^2 = (S_i S_j)^37 = I.

Original entry on oeis.org

1, 30, 870, 25230, 731670, 21218430, 615334470, 17844699630, 517496289270, 15007392388830, 435214379276070, 12621216999006030, 366015292971174870, 10614443496164071230, 307818861388758065670, 8926746980273983904430
Offset: 0

Views

Author

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

Keywords

Comments

The initial terms coincide with those of A170749, although the two sequences are eventually different.
Computed with MAGMA using commands similar to those used to compute A154638.

Programs

Formula

G.f. (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)/(406*t^37 - 28*t^36 - 28*t^35 -
28*t^34 - 28*t^33 - 28*t^32 - 28*t^31 - 28*t^30 - 28*t^29 - 28*t^28 -
28*t^27 - 28*t^26 - 28*t^25 - 28*t^24 - 28*t^23 - 28*t^22 - 28*t^21 -
28*t^20 - 28*t^19 - 28*t^18 - 28*t^17 - 28*t^16 - 28*t^15 - 28*t^14 -
28*t^13 - 28*t^12 - 28*t^11 - 28*t^10 - 28*t^9 - 28*t^8 - 28*t^7 -
28*t^6 - 28*t^5 - 28*t^4 - 28*t^3 - 28*t^2 - 28*t + 1)

A170135 Number of reduced words of length n in Coxeter group on 30 generators S_i with relations (S_i)^2 = (S_i S_j)^38 = I.

Original entry on oeis.org

1, 30, 870, 25230, 731670, 21218430, 615334470, 17844699630, 517496289270, 15007392388830, 435214379276070, 12621216999006030, 366015292971174870, 10614443496164071230, 307818861388758065670, 8926746980273983904430
Offset: 0

Views

Author

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

Keywords

Comments

The initial terms coincide with those of A170749, although the two sequences are eventually different.
Computed with MAGMA using commands similar to those used to compute A154638.

Programs

Formula

G.f. (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)/(406*t^38 - 28*t^37 -
28*t^36 - 28*t^35 - 28*t^34 - 28*t^33 - 28*t^32 - 28*t^31 - 28*t^30 -
28*t^29 - 28*t^28 - 28*t^27 - 28*t^26 - 28*t^25 - 28*t^24 - 28*t^23 -
28*t^22 - 28*t^21 - 28*t^20 - 28*t^19 - 28*t^18 - 28*t^17 - 28*t^16 -
28*t^15 - 28*t^14 - 28*t^13 - 28*t^12 - 28*t^11 - 28*t^10 - 28*t^9 -
28*t^8 - 28*t^7 - 28*t^6 - 28*t^5 - 28*t^4 - 28*t^3 - 28*t^2 - 28*t + 1)
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