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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A168701 Number of reduced words of length n in Coxeter group on 24 generators S_i with relations (S_i)^2 = (S_i S_j)^17 = I.

Original entry on oeis.org

1, 24, 552, 12696, 292008, 6716184, 154472232, 3552861336, 81715810728, 1879463646744, 43227663875112, 994236269127576, 22867434189934248, 525950986368487704, 12096872686475217192, 278228071788929995416
Offset: 0

Views

Author

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

Keywords

Comments

The initial terms coincide with those of A170743, although the two sequences are eventually different.
First disagreement at index 17: a(17) = 147182649976343967574788, A170743(17) = 147182649976343967575064. - Klaus Brockhaus, Mar 30 2011
Computed with MAGMA using commands similar to those used to compute A154638.

Links

Crossrefs

Cf. A170743 (G.f.: (1+x)/(1-23*x)).

Programs

  • Mathematica
    coxG[{17,253,-22}] (* The coxG program is at A169452 *) (* Harvey P. Dale, Apr 29 2016 *)
CoefficientList[Series[(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)/(253*t^17 - 22*t^16 - 22*t^15 - 22*t^14 - 22*t^13 - 22*t^12 - 22*t^11 - 22*t^10 - 22*t^9 - 22*t^8 - 22*t^7 - 22*t^6 - 22*t^5 - 22*t^4 - 22*t^3 - 22*t^2 - 22*t + 1), {t,0,50}], t] (* G. C. Greubel, Aug 04 2016 *)

Formula

G.f.: (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)/( 253*t^17 - 22*t^16 - 22*t^15 - 22*t^14 - 22*t^13 - 22*t^12 - 22*t^11 - 22*t^10 - 22*t^9 - 22*t^8 - 22*t^7 - 22*t^6 -22*t^5 -22*t^4 -22*t^3 -22*t^2 -22*t +1).

A168749 Number of reduced words of length n in Coxeter group on 24 generators S_i with relations (S_i)^2 = (S_i S_j)^18 = I.

Original entry on oeis.org

1, 24, 552, 12696, 292008, 6716184, 154472232, 3552861336, 81715810728, 1879463646744, 43227663875112, 994236269127576, 22867434189934248, 525950986368487704, 12096872686475217192, 278228071788929995416
Offset: 0

Views

Author

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

Keywords

Comments

The initial terms coincide with those of A170743, although the two sequences are eventually different.
First disagreement at index 18: a(18) = 3385200949455911254226196, A170743(18) = 3385200949455911254226472. - Klaus Brockhaus, Mar 26 2011
Computed with MAGMA using commands similar to those used to compute A154638.

Links

Crossrefs

Cf. A170743 (G.f.: (1+x)/(1-23*x)).

Programs

  • Mathematica
    coxG[{18,253,-22}] (* The coxG program is at A169452 *) (* Harvey P. Dale, Dec 19 2014 *)
CoefficientList[Series[(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)/(253*t^18 - 22*t^17 - 22*t^16 - 22*t^15 - 22*t^14 - 22*t^13 - 22*t^12 - 22*t^11 - 22*t^10 - 22*t^9 - 22*t^8 - 22*t^7 - 22*t^6 - 22*t^5 - 22*t^4 - 22*t^3 - 22*t^2 - 22*t + 1), {t, 0, 50}], t] (* G. C. Greubel, Aug 10 2016 *)

Formula

G.f.: (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)/(253*t^18 - 22*t^17 - 22*t^16 - 22*t^15 - 22*t^14 - 22*t^13 - 22*t^12 - 22*t^11 - 22*t^10 - 22*t^9 - 22*t^8 - 22*t^7 - 22*t^6 - 22*t^5 - 22*t^4 - 22*t^3 - 22*t^2 - 22*t + 1).

A168797 Number of reduced words of length n in Coxeter group on 24 generators S_i with relations (S_i)^2 = (S_i S_j)^19 = I.

Original entry on oeis.org

1, 24, 552, 12696, 292008, 6716184, 154472232, 3552861336, 81715810728, 1879463646744, 43227663875112, 994236269127576, 22867434189934248, 525950986368487704, 12096872686475217192, 278228071788929995416
Offset: 0

Views

Author

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

Keywords

Comments

The initial terms coincide with those of A170743, although the two sequences are eventually different.
First disagreement at index 19: a(19) = 77859621837485958847208580, A170743(19) = 77859621837485958847208856. - Klaus Brockhaus, Apr 01 2011
Computed with MAGMA using commands similar to those used to compute A154638.

Links

Crossrefs

Cf. A170743 (G.f.: (1+x)/(1-23*x)).

Programs

  • Mathematica
    CoefficientList[Series[(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)/(253*t^19 - 22*t^18 - 22*t^17 - 22*t^16 - 22*t^15 - 22*t^14 - 22*t^13 - 22*t^12 - 22*t^11 - 22*t^10 - 22*t^9 - 22*t^8 - 22*t^7 - 22*t^6 - 22*t^5 - 22*t^4 - 22*t^3 - 22*t^2 - 22*t + 1), {t, 0, 50}], t] (* G. C. Greubel, Aug 16 2016 *)
coxG[{19,253,-22}] (* The coxG program is at A169452 *) (* Harvey P. Dale, Feb 09 2025 *)

Formula

G.f.: (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)/(253*t^19 - 22*t^18 - 22*t^17 - 22*t^16 - 22*t^15 - 22*t^14 - 22*t^13 - 22*t^12 - 22*t^11 - 22*t^10 - 22*t^9 - 22*t^8 - 22*t^7 - 22*t^6 - 22*t^5 - 22*t^4 - 22*t^3 - 22*t^2 - 22*t + 1).

A169133 Number of reduced words of length n in Coxeter group on 24 generators S_i with relations (S_i)^2 = (S_i S_j)^26 = I.

Original entry on oeis.org

1, 24, 552, 12696, 292008, 6716184, 154472232, 3552861336, 81715810728, 1879463646744, 43227663875112, 994236269127576, 22867434189934248, 525950986368487704, 12096872686475217192, 278228071788929995416
Offset: 0

Views

Author

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

Keywords

Comments

The initial terms coincide with those of A170743, although the two sequences are eventually different.
First disagreement at index 26: a(26) = 265098421726069091188171497832558356, A170743(26) = 265098421726069091188171497832558632. - Klaus Brockhaus, Apr 30 2011
Computed with MAGMA using commands similar to those used to compute A154638.

Links

Crossrefs

Cf. A170743 (G.f.: (1+x)/(1-23*x)).

Programs

  • Mathematica
    With[{num=Total[2t^Range[25]]+t^26+1,den=Total[-22 t^Range[25]]+ 253t^26+1}, CoefficientList[Series[num/den,{t,0,30}],t]] (* Harvey P. Dale, Feb 27 2012 *)

Formula

G.f.: (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)/(253*t^26 - 22*t^25 - 22*t^24 - 22*t^23 - 22*t^22 - 22*t^21 - 22*t^20 - 22*t^19 - 22*t^18 - 22*t^17 - 22*t^16 - 22*t^15 - 22*t^14 - 22*t^13 - 22*t^12 - 22*t^11 - 22*t^10 - 22*t^9 - 22*t^8 - 22*t^7 - 22*t^6 - 22*t^5 - 22*t^4 - 22*t^3 - 22*t^2 - 22*t + 1).

A170705 Number of reduced words of length n in Coxeter group on 24 generators S_i with relations (S_i)^2 = (S_i S_j)^50 = I.

Original entry on oeis.org

1, 24, 552, 12696, 292008, 6716184, 154472232, 3552861336, 81715810728, 1879463646744, 43227663875112, 994236269127576, 22867434189934248, 525950986368487704, 12096872686475217192, 278228071788929995416
Offset: 0

Views

Author

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

Keywords

Comments

The initial terms coincide with those of A170743, although the two sequences are eventually different.
Computed with MAGMA using commands similar to those used to compute A154638.
About the initial comment, first disagreement is at index 50 and the difference is 276. - Vincenzo Librandi, Dec 08 2012

Links

Programs

  • Mathematica
    With[{num = Total[2 t^Range[49]] + t^50 + 1, den = Total[-22 t^Range[49]] + 253t^50 + 1}, CoefficientList[Series[num/den, {t, 0, 200}], t]] (* Vincenzo Librandi, Dec 08 2012 *)
coxG[{50,253,-22}] (* The coxG program is at A169452 *) (* Harvey P. Dale, Dec 31 2016 *)

Formula

G.f. (t^50 + 2*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)/(253*t^50 - 22*t^49 - 22*t^48 - 22*t^47 - 22*t^46 - 22*t^45 -
22*t^44 - 22*t^43 - 22*t^42 - 22*t^41 - 22*t^40 - 22*t^39 - 22*t^38 -
22*t^37 - 22*t^36 - 22*t^35 - 22*t^34 - 22*t^33 - 22*t^32 - 22*t^31 -
22*t^30 - 22*t^29 - 22*t^28 - 22*t^27 - 22*t^26 - 22*t^25 - 22*t^24 -
22*t^23 - 22*t^22 - 22*t^21 - 22*t^20 - 22*t^19 - 22*t^18 - 22*t^17 -
22*t^16 - 22*t^15 - 22*t^14 - 22*t^13 - 22*t^12 - 22*t^11 - 22*t^10 -
22*t^9 - 22*t^8 - 22*t^7 - 22*t^6 - 22*t^5 - 22*t^4 - 22*t^3 - 22*t^2 -
22*t + 1)

A162810 Number of reduced words of length n in Coxeter group on 24 generators S_i with relations (S_i)^2 = (S_i S_j)^3 = I.

Original entry on oeis.org

1, 24, 552, 12420, 279312, 6278448, 141128460, 3172286040, 71306671656, 1602831568932, 36028452924816, 809847670933488, 18203758337942892, 409184133605301912, 9197642162005213224, 206744627643931781316
Offset: 0

Views

Author

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

Keywords

Comments

The initial terms coincide with those of A170743, although the two sequences are eventually different.
Computed with MAGMA using commands similar to those used to compute A154638.

Links

Formula

G.f.: (t^3 + 2*t^2 + 2*t + 1)/(253*t^3 - 22*t^2 - 22*t + 1)

A163174 Number of reduced words of length n in Coxeter group on 24 generators S_i with relations (S_i)^2 = (S_i S_j)^4 = I.

Original entry on oeis.org

1, 24, 552, 12696, 291732, 6703488, 154034496, 3539441664, 81330144060, 1868823662376, 42942280730712, 986738081076264, 22673505553878564, 520997277758500752, 11971601073631152624, 275086336118245407888
Offset: 0

Views

Author

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

Keywords

Comments

The initial terms coincide with those of A170743, although the two sequences are eventually different.
Computed with MAGMA using commands similar to those used to compute A154638.

Links

Programs

  • Mathematica
    CoefficientList[Series[(t^4 + 2 t^3 + 2 t^2 + 2 t + 1)/(253 t^4 - 22 t^3 - 22 t^2 - 22 t + 1), {t, 0, 20}], t] (* Jinyuan Wang, Mar 23 2020 *)

Formula

G.f.: (t^4 + 2*t^3 + 2*t^2 + 2*t + 1)/(253*t^4 - 22*t^3 - 22*t^2 - 22*t + 1).

A164637 Number of reduced words of length n in Coxeter group on 24 generators S_i with relations (S_i)^2 = (S_i S_j)^7 = I.

Original entry on oeis.org

1, 24, 552, 12696, 292008, 6716184, 154472232, 3552861060, 81715798032, 1879463209008, 43227650455440, 994235883385008, 22867423544782608, 525950700749330736, 12096865179279290124, 278227877550453062232
Offset: 0

Views

Author

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

Keywords

Comments

The initial terms coincide with those of A170743, 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^7 + 2*t^6 + 2*t^5 + 2*t^4 + 2*t^3 + 2*t^2 + 2*t + 1)/(253*t^7 - 22*t^6 - 22*t^5 - 22*t^4 - 22*t^3 - 22*t^2 - 22*t + 1).

A164959 Number of reduced words of length n in Coxeter group on 24 generators S_i with relations (S_i)^2 = (S_i S_j)^8 = I.

Original entry on oeis.org

1, 24, 552, 12696, 292008, 6716184, 154472232, 3552861336, 81715810452, 1879463634048, 43227663437376, 994236255707904, 22867433804191680, 525950975723336064, 12096872400856060224, 278228064281733992448
Offset: 0

Views

Author

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

Keywords

Comments

The initial terms coincide with those of A170743, 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^8 + 2*t^7 + 2*t^6 + 2*t^5 + 2*t^4 + 2*t^3 + 2*t^2 + 2*t + 1)/(253*t^8 -
22*t^7 - 22*t^6 - 22*t^5 - 22*t^4 - 22*t^3 - 22*t^2 - 22*t + 1)

A165366 Number of reduced words of length n in Coxeter group on 24 generators S_i with relations (S_i)^2 = (S_i S_j)^9 = I.

Original entry on oeis.org

1, 24, 552, 12696, 292008, 6716184, 154472232, 3552861336, 81715810728, 1879463646468, 43227663862416, 994236268689840, 22867434176514576, 525950985982745136, 12096872675830065552, 278228071503310838448
Offset: 0

Views

Author

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

Keywords

Comments

The initial terms coincide with those of A170743, although the two sequences are eventually different.
Computed with MAGMA using commands similar to those used to compute A154638.

Links

Formula

G.f. (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)/(253*t^9 - 22*t^8 - 22*t^7 - 22*t^6 - 22*t^5 - 22*t^4 - 22*t^3 -
22*t^2 - 22*t + 1)
Previous Showing 11-20 of 49 results. Next

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