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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A169371 Number of reduced words of length n in Coxeter group on 22 generators S_i with relations (S_i)^2 = (S_i S_j)^31 = I.

Original entry on oeis.org

1, 22, 462, 9702, 203742, 4278582, 89850222, 1886854662, 39623947902, 832102905942, 17474161024782, 366957381520422, 7706105011928862, 161828205250506102, 3398392310260628142, 71366238515473190982
Offset: 0

Views

Author

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

Keywords

Comments

The initial terms coincide with those of A170741, although the two sequences are eventually different.
First disagreement at index 31: a(31) = 102094306360577610211441129338452806400991, A170741(31) = 102094306360577610211441129338452806401222. - Klaus Brockhaus, Jun 17 2011
Computed with Magma using commands similar to those used to compute A154638.

Crossrefs

Cf. A170741 (G.f.: (1+x)/(1-21*x)).

Programs

  • Mathematica
    With[{num=Total[2t^Range[30]]+t^31+1,den=Total[-20 t^Range[30]]+ 210t^31+ 1}, CoefficientList[Series[num/den,{t,0,20}],t]] (* Harvey P. Dale, Sep 21 2011 *)

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)/(210*t^31 - 20*t^30 - 20*t^29 - 20*t^28 - 20*t^27 - 20*t^26 - 20*t^25 - 20*t^24 - 20*t^23 - 20*t^22 - 20*t^21 - 20*t^20 - 20*t^19 - 20*t^18 - 20*t^17 - 20*t^16 - 20*t^15 - 20*t^14 - 20*t^13 - 20*t^12 - 20*t^11 - 20*t^10 - 20*t^9 - 20*t^8 - 20*t^7 - 20*t^6 - 20*t^5 - 20*t^4 - 20*t^3 - 20*t^2 - 20*t + 1).

A169419 Number of reduced words of length n in Coxeter group on 22 generators S_i with relations (S_i)^2 = (S_i S_j)^32 = I.

Original entry on oeis.org

1, 22, 462, 9702, 203742, 4278582, 89850222, 1886854662, 39623947902, 832102905942, 17474161024782, 366957381520422, 7706105011928862, 161828205250506102, 3398392310260628142, 71366238515473190982
Offset: 0

Views

Author

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

Keywords

Comments

The initial terms coincide with those of A170741, although the two sequences are eventually different.
First disagreement is at index 32, the difference is 231. - Klaus Brockhaus, Jun 27 2011
Computed with Magma using commands similar to those used to compute A154638.

Crossrefs

Cf. A170741 (G.f.: (1+x)/(1-21*x) ).

Programs

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)/(210*t^32 - 20*t^31 - 20*t^30 - 20*t^29 - 20*t^28 - 20*t^27 - 20*t^26 - 20*t^25 - 20*t^24 - 20*t^23 - 20*t^22 - 20*t^21 - 20*t^20 - 20*t^19 - 20*t^18 - 20*t^17 - 20*t^16 - 20*t^15 - 20*t^14 - 20*t^13 - 20*t^12 - 20*t^11 - 20*t^10 - 20*t^9 - 20*t^8 - 20*t^7 - 20*t^6 - 20*t^5 - 20*t^4 - 20*t^3 - 20*t^2 - 20*t + 1).
G.f.: (1+2*sum(k=1..31, x^k)+x^32)/(1-20*sum(k=1..31, x^k)+210*x^32).

A169467 Number of reduced words of length n in Coxeter group on 22 generators S_i with relations (S_i)^2 = (S_i S_j)^33 = I.

Original entry on oeis.org

1, 22, 462, 9702, 203742, 4278582, 89850222, 1886854662, 39623947902, 832102905942, 17474161024782, 366957381520422, 7706105011928862, 161828205250506102, 3398392310260628142, 71366238515473190982
Offset: 0

Views

Author

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

Keywords

Comments

The initial terms coincide with those of A170741, 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)/(210*t^33 - 20*t^32 - 20*t^31 - 20*t^30 - 20*t^29 - 20*t^28 - 20*t^27
- 20*t^26 - 20*t^25 - 20*t^24 - 20*t^23 - 20*t^22 - 20*t^21 - 20*t^20 -
20*t^19 - 20*t^18 - 20*t^17 - 20*t^16 - 20*t^15 - 20*t^14 - 20*t^13 -
20*t^12 - 20*t^11 - 20*t^10 - 20*t^9 - 20*t^8 - 20*t^7 - 20*t^6 - 20*t^5
- 20*t^4 - 20*t^3 - 20*t^2 - 20*t + 1)

A169515 Number of reduced words of length n in Coxeter group on 22 generators S_i with relations (S_i)^2 = (S_i S_j)^34 = I.

Original entry on oeis.org

1, 22, 462, 9702, 203742, 4278582, 89850222, 1886854662, 39623947902, 832102905942, 17474161024782, 366957381520422, 7706105011928862, 161828205250506102, 3398392310260628142, 71366238515473190982
Offset: 0

Views

Author

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

Keywords

Comments

The initial terms coincide with those of A170741, 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)/(210*t^34 - 20*t^33 - 20*t^32 - 20*t^31 - 20*t^30 - 20*t^29 -
20*t^28 - 20*t^27 - 20*t^26 - 20*t^25 - 20*t^24 - 20*t^23 - 20*t^22 -
20*t^21 - 20*t^20 - 20*t^19 - 20*t^18 - 20*t^17 - 20*t^16 - 20*t^15 -
20*t^14 - 20*t^13 - 20*t^12 - 20*t^11 - 20*t^10 - 20*t^9 - 20*t^8 -
20*t^7 - 20*t^6 - 20*t^5 - 20*t^4 - 20*t^3 - 20*t^2 - 20*t + 1)

A169563 Number of reduced words of length n in Coxeter group on 22 generators S_i with relations (S_i)^2 = (S_i S_j)^35 = I.

Original entry on oeis.org

1, 22, 462, 9702, 203742, 4278582, 89850222, 1886854662, 39623947902, 832102905942, 17474161024782, 366957381520422, 7706105011928862, 161828205250506102, 3398392310260628142, 71366238515473190982
Offset: 0

Views

Author

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

Keywords

Comments

The initial terms coincide with those of A170741, although the two sequences are eventually different.
Computed with MAGMA using commands similar to those used to compute A154638.

Programs

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)/(210*t^35 - 20*t^34 - 20*t^33 - 20*t^32 - 20*t^31 -
20*t^30 - 20*t^29 - 20*t^28 - 20*t^27 - 20*t^26 - 20*t^25 - 20*t^24 -
20*t^23 - 20*t^22 - 20*t^21 - 20*t^20 - 20*t^19 - 20*t^18 - 20*t^17 -
20*t^16 - 20*t^15 - 20*t^14 - 20*t^13 - 20*t^12 - 20*t^11 - 20*t^10 -
20*t^9 - 20*t^8 - 20*t^7 - 20*t^6 - 20*t^5 - 20*t^4 - 20*t^3 - 20*t^2 -
20*t + 1)

A170031 Number of reduced words of length n in Coxeter group on 22 generators S_i with relations (S_i)^2 = (S_i S_j)^36 = I.

Original entry on oeis.org

1, 22, 462, 9702, 203742, 4278582, 89850222, 1886854662, 39623947902, 832102905942, 17474161024782, 366957381520422, 7706105011928862, 161828205250506102, 3398392310260628142, 71366238515473190982
Offset: 0

Views

Author

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

Keywords

Comments

The initial terms coincide with those of A170741, 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)/(210*t^36 - 20*t^35 - 20*t^34 - 20*t^33 -
20*t^32 - 20*t^31 - 20*t^30 - 20*t^29 - 20*t^28 - 20*t^27 - 20*t^26 -
20*t^25 - 20*t^24 - 20*t^23 - 20*t^22 - 20*t^21 - 20*t^20 - 20*t^19 -
20*t^18 - 20*t^17 - 20*t^16 - 20*t^15 - 20*t^14 - 20*t^13 - 20*t^12 -
20*t^11 - 20*t^10 - 20*t^9 - 20*t^8 - 20*t^7 - 20*t^6 - 20*t^5 - 20*t^4
- 20*t^3 - 20*t^2 - 20*t + 1)

A170079 Number of reduced words of length n in Coxeter group on 22 generators S_i with relations (S_i)^2 = (S_i S_j)^37 = I.

Original entry on oeis.org

1, 22, 462, 9702, 203742, 4278582, 89850222, 1886854662, 39623947902, 832102905942, 17474161024782, 366957381520422, 7706105011928862, 161828205250506102, 3398392310260628142, 71366238515473190982
Offset: 0

Views

Author

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

Keywords

Comments

The initial terms coincide with those of A170741, although the two sequences are eventually different.
Computed with MAGMA using commands similar to those used to compute A154638.

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)/(210*t^37 - 20*t^36 - 20*t^35 -
20*t^34 - 20*t^33 - 20*t^32 - 20*t^31 - 20*t^30 - 20*t^29 - 20*t^28 -
20*t^27 - 20*t^26 - 20*t^25 - 20*t^24 - 20*t^23 - 20*t^22 - 20*t^21 -
20*t^20 - 20*t^19 - 20*t^18 - 20*t^17 - 20*t^16 - 20*t^15 - 20*t^14 -
20*t^13 - 20*t^12 - 20*t^11 - 20*t^10 - 20*t^9 - 20*t^8 - 20*t^7 -
20*t^6 - 20*t^5 - 20*t^4 - 20*t^3 - 20*t^2 - 20*t + 1)

A170127 Number of reduced words of length n in Coxeter group on 22 generators S_i with relations (S_i)^2 = (S_i S_j)^38 = I.

Original entry on oeis.org

1, 22, 462, 9702, 203742, 4278582, 89850222, 1886854662, 39623947902, 832102905942, 17474161024782, 366957381520422, 7706105011928862, 161828205250506102, 3398392310260628142, 71366238515473190982
Offset: 0

Views

Author

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

Keywords

Comments

The initial terms coincide with those of A170741, although the two sequences are eventually different.
Computed with MAGMA using commands similar to those used to compute A154638.

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)/(210*t^38 - 20*t^37 -
20*t^36 - 20*t^35 - 20*t^34 - 20*t^33 - 20*t^32 - 20*t^31 - 20*t^30 -
20*t^29 - 20*t^28 - 20*t^27 - 20*t^26 - 20*t^25 - 20*t^24 - 20*t^23 -
20*t^22 - 20*t^21 - 20*t^20 - 20*t^19 - 20*t^18 - 20*t^17 - 20*t^16 -
20*t^15 - 20*t^14 - 20*t^13 - 20*t^12 - 20*t^11 - 20*t^10 - 20*t^9 -
20*t^8 - 20*t^7 - 20*t^6 - 20*t^5 - 20*t^4 - 20*t^3 - 20*t^2 - 20*t + 1)

A170175 Number of reduced words of length n in Coxeter group on 22 generators S_i with relations (S_i)^2 = (S_i S_j)^39 = I.

Original entry on oeis.org

1, 22, 462, 9702, 203742, 4278582, 89850222, 1886854662, 39623947902, 832102905942, 17474161024782, 366957381520422, 7706105011928862, 161828205250506102, 3398392310260628142, 71366238515473190982
Offset: 0

Views

Author

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

Keywords

Comments

The initial terms coincide with those of A170741, 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[38]]+t^39+1,den=Total[-20 t^Range[38]]+210t^39+ 1},CoefficientList[Series[num/den,{t,0,30}],t]] (* Harvey P. Dale, Nov 25 2013 *)

Formula

G.f. (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)/(210*t^39 -
20*t^38 - 20*t^37 - 20*t^36 - 20*t^35 - 20*t^34 - 20*t^33 - 20*t^32 -
20*t^31 - 20*t^30 - 20*t^29 - 20*t^28 - 20*t^27 - 20*t^26 - 20*t^25 -
20*t^24 - 20*t^23 - 20*t^22 - 20*t^21 - 20*t^20 - 20*t^19 - 20*t^18 -
20*t^17 - 20*t^16 - 20*t^15 - 20*t^14 - 20*t^13 - 20*t^12 - 20*t^11 -
20*t^10 - 20*t^9 - 20*t^8 - 20*t^7 - 20*t^6 - 20*t^5 - 20*t^4 - 20*t^3 -
20*t^2 - 20*t + 1)

A170223 Number of reduced words of length n in Coxeter group on 22 generators S_i with relations (S_i)^2 = (S_i S_j)^40 = I.

Original entry on oeis.org

1, 22, 462, 9702, 203742, 4278582, 89850222, 1886854662, 39623947902, 832102905942, 17474161024782, 366957381520422, 7706105011928862, 161828205250506102, 3398392310260628142, 71366238515473190982
Offset: 0

Views

Author

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

Keywords

Comments

The initial terms coincide with those of A170741, although the two sequences are eventually different.
Computed with MAGMA using commands similar to those used to compute A154638.

Programs

Formula

G.f. (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)/(210*t^40 - 20*t^39 - 20*t^38 - 20*t^37 - 20*t^36 - 20*t^35 - 20*t^34
- 20*t^33 - 20*t^32 - 20*t^31 - 20*t^30 - 20*t^29 - 20*t^28 - 20*t^27 -
20*t^26 - 20*t^25 - 20*t^24 - 20*t^23 - 20*t^22 - 20*t^21 - 20*t^20 -
20*t^19 - 20*t^18 - 20*t^17 - 20*t^16 - 20*t^15 - 20*t^14 - 20*t^13 -
20*t^12 - 20*t^11 - 20*t^10 - 20*t^9 - 20*t^8 - 20*t^7 - 20*t^6 - 20*t^5
- 20*t^4 - 20*t^3 - 20*t^2 - 20*t + 1)
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