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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A170277 Number of reduced words of length n in Coxeter group on 28 generators S_i with relations (S_i)^2 = (S_i S_j)^41 = I.

Original entry on oeis.org

1, 28, 756, 20412, 551124, 14880348, 401769396, 10847773692, 292889889684, 7908027021468, 213516729579636, 5764951698650172, 155653695863554644, 4202649788315975388, 113471544284531335476, 3063731695682346057852
Offset: 0

Views

Author

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

Keywords

Comments

The initial terms coincide with those of A170747, 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)/(351*t^41 - 26*t^40 - 26*t^39 - 26*t^38 - 26*t^37 - 26*t^36 - 26*t^35
- 26*t^34 - 26*t^33 - 26*t^32 - 26*t^31 - 26*t^30 - 26*t^29 - 26*t^28 -
26*t^27 - 26*t^26 - 26*t^25 - 26*t^24 - 26*t^23 - 26*t^22 - 26*t^21 -
26*t^20 - 26*t^19 - 26*t^18 - 26*t^17 - 26*t^16 - 26*t^15 - 26*t^14 -
26*t^13 - 26*t^12 - 26*t^11 - 26*t^10 - 26*t^9 - 26*t^8 - 26*t^7 -
26*t^6 - 26*t^5 - 26*t^4 - 26*t^3 - 26*t^2 - 26*t + 1)

A170325 Number of reduced words of length n in Coxeter group on 28 generators S_i with relations (S_i)^2 = (S_i S_j)^42 = I.

Original entry on oeis.org

1, 28, 756, 20412, 551124, 14880348, 401769396, 10847773692, 292889889684, 7908027021468, 213516729579636, 5764951698650172, 155653695863554644, 4202649788315975388, 113471544284531335476, 3063731695682346057852
Offset: 0

Views

Author

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

Keywords

Comments

The initial terms coincide with those of A170747, 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^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)/(351*t^42 - 26*t^41 - 26*t^40 - 26*t^39 - 26*t^38 - 26*t^37 -
26*t^36 - 26*t^35 - 26*t^34 - 26*t^33 - 26*t^32 - 26*t^31 - 26*t^30 -
26*t^29 - 26*t^28 - 26*t^27 - 26*t^26 - 26*t^25 - 26*t^24 - 26*t^23 -
26*t^22 - 26*t^21 - 26*t^20 - 26*t^19 - 26*t^18 - 26*t^17 - 26*t^16 -
26*t^15 - 26*t^14 - 26*t^13 - 26*t^12 - 26*t^11 - 26*t^10 - 26*t^9 -
26*t^8 - 26*t^7 - 26*t^6 - 26*t^5 - 26*t^4 - 26*t^3 - 26*t^2 - 26*t + 1)

A170373 Number of reduced words of length n in Coxeter group on 28 generators S_i with relations (S_i)^2 = (S_i S_j)^43 = I.

Original entry on oeis.org

1, 28, 756, 20412, 551124, 14880348, 401769396, 10847773692, 292889889684, 7908027021468, 213516729579636, 5764951698650172, 155653695863554644, 4202649788315975388, 113471544284531335476, 3063731695682346057852
Offset: 0

Views

Author

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

Keywords

Comments

The initial terms coincide with those of A170747, 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[-26 t^Range[42]]+351t^43+ 1},CoefficientList[Series[num/den,{t,0,30}],t]] (* Harvey P. Dale, May 04 2014 *)

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)/(351*t^43 - 26*t^42 - 26*t^41 - 26*t^40 - 26*t^39 -
26*t^38 - 26*t^37 - 26*t^36 - 26*t^35 - 26*t^34 - 26*t^33 - 26*t^32 -
26*t^31 - 26*t^30 - 26*t^29 - 26*t^28 - 26*t^27 - 26*t^26 - 26*t^25 -
26*t^24 - 26*t^23 - 26*t^22 - 26*t^21 - 26*t^20 - 26*t^19 - 26*t^18 -
26*t^17 - 26*t^16 - 26*t^15 - 26*t^14 - 26*t^13 - 26*t^12 - 26*t^11 -
26*t^10 - 26*t^9 - 26*t^8 - 26*t^7 - 26*t^6 - 26*t^5 - 26*t^4 - 26*t^3 -
26*t^2 - 26*t + 1)

A170421 Number of reduced words of length n in Coxeter group on 28 generators S_i with relations (S_i)^2 = (S_i S_j)^44 = I.

Original entry on oeis.org

1, 28, 756, 20412, 551124, 14880348, 401769396, 10847773692, 292889889684, 7908027021468, 213516729579636, 5764951698650172, 155653695863554644, 4202649788315975388, 113471544284531335476, 3063731695682346057852
Offset: 0

Views

Author

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

Keywords

Comments

The initial terms coincide with those of A170747, 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^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)/(351*t^44 - 26*t^43 - 26*t^42 - 26*t^41 -
26*t^40 - 26*t^39 - 26*t^38 - 26*t^37 - 26*t^36 - 26*t^35 - 26*t^34 -
26*t^33 - 26*t^32 - 26*t^31 - 26*t^30 - 26*t^29 - 26*t^28 - 26*t^27 -
26*t^26 - 26*t^25 - 26*t^24 - 26*t^23 - 26*t^22 - 26*t^21 - 26*t^20 -
26*t^19 - 26*t^18 - 26*t^17 - 26*t^16 - 26*t^15 - 26*t^14 - 26*t^13 -
26*t^12 - 26*t^11 - 26*t^10 - 26*t^9 - 26*t^8 - 26*t^7 - 26*t^6 - 26*t^5
- 26*t^4 - 26*t^3 - 26*t^2 - 26*t + 1)

A170469 Number of reduced words of length n in Coxeter group on 28 generators S_i with relations (S_i)^2 = (S_i S_j)^45 = I.

Original entry on oeis.org

1, 28, 756, 20412, 551124, 14880348, 401769396, 10847773692, 292889889684, 7908027021468, 213516729579636, 5764951698650172, 155653695863554644, 4202649788315975388, 113471544284531335476, 3063731695682346057852
Offset: 0

Views

Author

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

Keywords

Comments

The initial terms coincide with those of A170747, 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^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)/(351*t^45 - 26*t^44 - 26*t^43 -
26*t^42 - 26*t^41 - 26*t^40 - 26*t^39 - 26*t^38 - 26*t^37 - 26*t^36 -
26*t^35 - 26*t^34 - 26*t^33 - 26*t^32 - 26*t^31 - 26*t^30 - 26*t^29 -
26*t^28 - 26*t^27 - 26*t^26 - 26*t^25 - 26*t^24 - 26*t^23 - 26*t^22 -
26*t^21 - 26*t^20 - 26*t^19 - 26*t^18 - 26*t^17 - 26*t^16 - 26*t^15 -
26*t^14 - 26*t^13 - 26*t^12 - 26*t^11 - 26*t^10 - 26*t^9 - 26*t^8 -
26*t^7 - 26*t^6 - 26*t^5 - 26*t^4 - 26*t^3 - 26*t^2 - 26*t + 1)

A170517 Number of reduced words of length n in Coxeter group on 28 generators S_i with relations (S_i)^2 = (S_i S_j)^46 = I.

Original entry on oeis.org

1, 28, 756, 20412, 551124, 14880348, 401769396, 10847773692, 292889889684, 7908027021468, 213516729579636, 5764951698650172, 155653695863554644, 4202649788315975388, 113471544284531335476, 3063731695682346057852
Offset: 0

Views

Author

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

Keywords

Comments

The initial terms coincide with those of A170747, 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[45]]+t^46+1,den=Total[-26 t^Range[45]]+ 351t^46+ 1},CoefficientList[Series[num/den,{t,0,30}],t]] (* Harvey P. Dale, Jan 27 2013 *)

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)/(351*t^46 - 26*t^45 -
26*t^44 - 26*t^43 - 26*t^42 - 26*t^41 - 26*t^40 - 26*t^39 - 26*t^38 -
26*t^37 - 26*t^36 - 26*t^35 - 26*t^34 - 26*t^33 - 26*t^32 - 26*t^31 -
26*t^30 - 26*t^29 - 26*t^28 - 26*t^27 - 26*t^26 - 26*t^25 - 26*t^24 -
26*t^23 - 26*t^22 - 26*t^21 - 26*t^20 - 26*t^19 - 26*t^18 - 26*t^17 -
26*t^16 - 26*t^15 - 26*t^14 - 26*t^13 - 26*t^12 - 26*t^11 - 26*t^10 -
26*t^9 - 26*t^8 - 26*t^7 - 26*t^6 - 26*t^5 - 26*t^4 - 26*t^3 - 26*t^2 -
26*t + 1)

A170565 Number of reduced words of length n in Coxeter group on 28 generators S_i with relations (S_i)^2 = (S_i S_j)^47 = I.

Original entry on oeis.org

1, 28, 756, 20412, 551124, 14880348, 401769396, 10847773692, 292889889684, 7908027021468, 213516729579636, 5764951698650172, 155653695863554644, 4202649788315975388, 113471544284531335476, 3063731695682346057852
Offset: 0

Views

Author

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

Keywords

Comments

The initial terms coincide with those of A170747, 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)/(351*t^47 -
26*t^46 - 26*t^45 - 26*t^44 - 26*t^43 - 26*t^42 - 26*t^41 - 26*t^40 -
26*t^39 - 26*t^38 - 26*t^37 - 26*t^36 - 26*t^35 - 26*t^34 - 26*t^33 -
26*t^32 - 26*t^31 - 26*t^30 - 26*t^29 - 26*t^28 - 26*t^27 - 26*t^26 -
26*t^25 - 26*t^24 - 26*t^23 - 26*t^22 - 26*t^21 - 26*t^20 - 26*t^19 -
26*t^18 - 26*t^17 - 26*t^16 - 26*t^15 - 26*t^14 - 26*t^13 - 26*t^12 -
26*t^11 - 26*t^10 - 26*t^9 - 26*t^8 - 26*t^7 - 26*t^6 - 26*t^5 - 26*t^4
- 26*t^3 - 26*t^2 - 26*t + 1)

A170613 Number of reduced words of length n in Coxeter group on 28 generators S_i with relations (S_i)^2 = (S_i S_j)^48 = I.

Original entry on oeis.org

1, 28, 756, 20412, 551124, 14880348, 401769396, 10847773692, 292889889684, 7908027021468, 213516729579636, 5764951698650172, 155653695863554644, 4202649788315975388, 113471544284531335476, 3063731695682346057852
Offset: 0

Views

Author

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

Keywords

Comments

The initial terms coincide with those of A170747, 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)/(351*t^48 - 26*t^47 - 26*t^46 - 26*t^45 - 26*t^44 - 26*t^43 - 26*t^42
- 26*t^41 - 26*t^40 - 26*t^39 - 26*t^38 - 26*t^37 - 26*t^36 - 26*t^35 -
26*t^34 - 26*t^33 - 26*t^32 - 26*t^31 - 26*t^30 - 26*t^29 - 26*t^28 -
26*t^27 - 26*t^26 - 26*t^25 - 26*t^24 - 26*t^23 - 26*t^22 - 26*t^21 -
26*t^20 - 26*t^19 - 26*t^18 - 26*t^17 - 26*t^16 - 26*t^15 - 26*t^14 -
26*t^13 - 26*t^12 - 26*t^11 - 26*t^10 - 26*t^9 - 26*t^8 - 26*t^7 -
26*t^6 - 26*t^5 - 26*t^4 - 26*t^3 - 26*t^2 - 26*t + 1)

A170661 Number of reduced words of length n in Coxeter group on 28 generators S_i with relations (S_i)^2 = (S_i S_j)^49 = I.

Original entry on oeis.org

1, 28, 756, 20412, 551124, 14880348, 401769396, 10847773692, 292889889684, 7908027021468, 213516729579636, 5764951698650172, 155653695863554644, 4202649788315975388, 113471544284531335476, 3063731695682346057852
Offset: 0

Views

Author

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

Keywords

Comments

The initial terms coincide with those of A170747, 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)/(351*t^49 - 26*t^48 - 26*t^47 - 26*t^46 - 26*t^45 - 26*t^44 - 26*t^43
- 26*t^42 - 26*t^41 - 26*t^40 - 26*t^39 - 26*t^38 - 26*t^37 - 26*t^36 -
26*t^35 - 26*t^34 - 26*t^33 - 26*t^32 - 26*t^31 - 26*t^30 - 26*t^29 -
26*t^28 - 26*t^27 - 26*t^26 - 26*t^25 - 26*t^24 - 26*t^23 - 26*t^22 -
26*t^21 - 26*t^20 - 26*t^19 - 26*t^18 - 26*t^17 - 26*t^16 - 26*t^15 -
26*t^14 - 26*t^13 - 26*t^12 - 26*t^11 - 26*t^10 - 26*t^9 - 26*t^8 -
26*t^7 - 26*t^6 - 26*t^5 - 26*t^4 - 26*t^3 - 26*t^2 - 26*t + 1)
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