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.

A170271 Number of reduced words of length n in Coxeter group on 22 generators S_i with relations (S_i)^2 = (S_i S_j)^41 = 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.

Links

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)/(210*t^41 - 20*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)

A170319 Number of reduced words of length n in Coxeter group on 22 generators S_i with relations (S_i)^2 = (S_i S_j)^42 = 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.

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)/(210*t^42 - 20*t^41 - 20*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)

A170367 Number of reduced words of length n in Coxeter group on 22 generators S_i with relations (S_i)^2 = (S_i S_j)^43 = 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.

Links

Programs

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)/(210*t^43 - 20*t^42 - 20*t^41 - 20*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)

A170415 Number of reduced words of length n in Coxeter group on 22 generators S_i with relations (S_i)^2 = (S_i S_j)^44 = 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.

Links

Programs

  • Mathematica
    With[{num=Total[2t^Range[43]]+t^44+1,den=Total[-20 t^Range[43]]+ 210t^44+ 1},CoefficientList[Series[num/den,{t,0,20}],t]] (* Harvey P. Dale, Feb 18 2013 *)

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)/(210*t^44 - 20*t^43 - 20*t^42 - 20*t^41 -
20*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)

A170463 Number of reduced words of length n in Coxeter group on 22 generators S_i with relations (S_i)^2 = (S_i S_j)^45 = 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.

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)/(210*t^45 - 20*t^44 - 20*t^43 -
20*t^42 - 20*t^41 - 20*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)

A170511 Number of reduced words of length n in Coxeter group on 22 generators S_i with relations (S_i)^2 = (S_i S_j)^46 = 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.

Links

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)/(210*t^46 - 20*t^45 -
20*t^44 - 20*t^43 - 20*t^42 - 20*t^41 - 20*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)

A170559 Number of reduced words of length n in Coxeter group on 22 generators S_i with relations (S_i)^2 = (S_i S_j)^47 = 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.

Links

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)/(210*t^47 -
20*t^46 - 20*t^45 - 20*t^44 - 20*t^43 - 20*t^42 - 20*t^41 - 20*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)

A170607 Number of reduced words of length n in Coxeter group on 22 generators S_i with relations (S_i)^2 = (S_i S_j)^48 = 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.

Links

Programs

  • Mathematica
    With[{num=Total[2t^Range[47]]+t^48+1,den=Total[-20 t^Range[47]]+210t^48+1}, CoefficientList[Series[num/den,{t,0,20}],t]] (* Harvey P. Dale, Mar 01 2012 *)

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)/(210*t^48 - 20*t^47 - 20*t^46 - 20*t^45 - 20*t^44 - 20*t^43 - 20*t^42
- 20*t^41 - 20*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)

A170655 Number of reduced words of length n in Coxeter group on 22 generators S_i with relations (S_i)^2 = (S_i S_j)^49 = 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.

Links

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)/(210*t^49 - 20*t^48 - 20*t^47 - 20*t^46 - 20*t^45 - 20*t^44 - 20*t^43
- 20*t^42 - 20*t^41 - 20*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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