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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A167879 Number of reduced words of length n in Coxeter group on 49 generators S_i with relations (S_i)^2 = (S_i S_j)^15 = I.

Original entry on oeis.org

1, 49, 2352, 112896, 5419008, 260112384, 12485394432, 599298932736, 28766348771328, 1380784741023744, 66277667569139712, 3181328043318706176, 152703746079297896448, 7329779811806299029504, 351829430966702353416192
Offset: 0

Views

Author

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

Keywords

Comments

The initial terms coincide with those of A170768, although the two sequences are eventually different.
Computed with MAGMA using commands similar to those used to compute A154638.

Links

Programs

  • Mathematica
    coxG[{15,1128,-47}] (* The coxG program is at A169452 *) (* Harvey P. Dale, May 05 2015 *)
CoefficientList[Series[(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)/(1128*t^15 - 47*t^14 - 47*t^13 - 47*t^12 - 47*t^11 - 47*t^10 - 47*t^9 - 47*t^8 - 47*t^7 - 47*t^6 - 47*t^5 - 47*t^4 - 47*t^3 - 47*t^2 - 47*t + 1), {t, 0, 50}], t] (* G. C. Greubel, Jun 29 2016 *)

Formula

G.f.: (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)/(1128*t^15 - 47*t^14 - 47*t^13 - 47*t^12 - 47*t^11 - 47*t^10 - 47*t^9 - 47*t^8 - 47*t^7 - 47*t^6 - 47*t^5 - 47*t^4 - 47*t^3 - 47*t^2 - 47*t + 1).

A168726 Number of reduced words of length n in Coxeter group on 49 generators S_i with relations (S_i)^2 = (S_i S_j)^17 = I.

Original entry on oeis.org

1, 49, 2352, 112896, 5419008, 260112384, 12485394432, 599298932736, 28766348771328, 1380784741023744, 66277667569139712, 3181328043318706176, 152703746079297896448, 7329779811806299029504, 351829430966702353416192
Offset: 0

Views

Author

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

Keywords

Comments

The initial terms coincide with those of A170768, although the two sequences are eventually different.
First disagreement at index 17: a(17) = 38909520429469546669003504488, A170768(17) = 38909520429469546669003505664. - Klaus Brockhaus, Mar 28 2011
Computed with MAGMA using commands similar to those used to compute A154638.

Links

Crossrefs

Cf. A170768 (G.f.: (1+x)/(1-48*x)).

Programs

  • Mathematica
    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)/(1128*t^17 - 47*t^16 - 47*t^15 - 47*t^14 - 47*t^13 - 47*t^12 - 47*t^11 - 47*t^10 - 47*t^9 - 47*t^8 - 47*t^7 - 47*t^6 - 47*t^5 - 47*t^4 - 47*t^3 - 47*t^2 - 47*t + 1), {t,0,50}], t] (* G. C. Greubel, Aug 06 2016 *)
coxG[{17,1128,-47}] (* The coxG program is at A169452 *) (* Harvey P. Dale, Jan 29 2017 *)

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)/(1128*t^17 - 47*t^16 - 47*t^15 - 47*t^14 - 47*t^13 - 47*t^12 - 47*t^11 - 47*t^10 - 47*t^9 - 47*t^8 - 47*t^7 - 47*t^6 - 47*t^5 - 47*t^4 - 47*t^3 - 47*t^2 - 47*t + 1).

A168774 Number of reduced words of length n in Coxeter group on 49 generators S_i with relations (S_i)^2 = (S_i S_j)^18 = I.

Original entry on oeis.org

1, 49, 2352, 112896, 5419008, 260112384, 12485394432, 599298932736, 28766348771328, 1380784741023744, 66277667569139712, 3181328043318706176, 152703746079297896448, 7329779811806299029504, 351829430966702353416192
Offset: 0

Views

Author

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

Keywords

Comments

The initial terms coincide with those of A170768, although the two sequences are eventually different.
First disagreement at index 18: a(18) = 1867656980614538240112168270696, A170768(18) = 1867656980614538240112168271872. - Klaus Brockhaus, Mar 25 2011
Computed with MAGMA using commands similar to those used to compute A154638.

Links

Crossrefs

Cf. A170768 (G.f.: (1+x)/(1-48*x)).

Programs

  • Mathematica
    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)/(1128*t^18 - 47*t^17 - 47*t^16 - 47*t^15 - 47*t^14 - 47*t^13 - 47*t^12 - 47*t^11 - 47*t^10 - 47*t^9 - 47*t^8 - 47*t^7 - 47*t^6 - 47*t^5 - 47*t^4 - 47*t^3 - 47*t^2 - 47*t + 1), {t, 0, 50}], t] (* G. C. Greubel, Aug 12 2016 *)
coxG[{18,1128,-47}] (* The coxG program is at A169452 *) (* Harvey P. Dale, Aug 21 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)/(1128*t^18 - 47*t^17 - 47*t^16 - 47*t^15 - 47*t^14 - 47*t^13 - 47*t^12 - 47*t^11 - 47*t^10 - 47*t^9 - 47*t^8 - 47*t^7 - 47*t^6 - 47*t^5 - 47*t^4 - 47*t^3 - 47*t^2 - 47*t + 1).

A168822 Number of reduced words of length n in Coxeter group on 49 generators S_i with relations (S_i)^2 = (S_i S_j)^19 = I.

Original entry on oeis.org

1, 49, 2352, 112896, 5419008, 260112384, 12485394432, 599298932736, 28766348771328, 1380784741023744, 66277667569139712, 3181328043318706176, 152703746079297896448, 7329779811806299029504, 351829430966702353416192
Offset: 0

Views

Author

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

Keywords

Comments

The initial terms coincide with those of A170768, although the two sequences are eventually different.
First disagreement at index 19: a(19) = 89647535069497835525384077048680, A170768(19) = 89647535069497835525384077049856. - Klaus Brockhaus, Apr 01 2011
Computed with MAGMA using commands similar to those used to compute A154638.

Links

Crossrefs

Cf. A170768 (G.f.: (1+x)/(1-48*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)/(1128*t^19 - 47*t^18 - 47*t^17 - 47*t^16 - 47*t^15 - 47*t^14 - 47*t^13 - 47*t^12 - 47*t^11 - 47*t^10 - 47*t^9 - 47*t^8 - 47*t^7 - 47*t^6 - 47*t^5 - 47*t^4 - 47*t^3 - 47*t^2 - 47*t + 1), {t,0,50}], t] (* G. C. Greubel, Nov 21 2016 *)

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)/(1128*t^19 - 47*t^18 - 47*t^17 - 47*t^16 - 47*t^15 - 47*t^14 - 47*t^13 - 47*t^12 - 47*t^11 - 47*t^10 - 47*t^9 - 47*t^8 - 47*t^7 - 47*t^6 - 47*t^5 - 47*t^4 - 47*t^3 - 47*t^2 - 47*t + 1).

A170730 Number of reduced words of length n in Coxeter group on 49 generators S_i with relations (S_i)^2 = (S_i S_j)^50 = I.

Original entry on oeis.org

1, 49, 2352, 112896, 5419008, 260112384, 12485394432, 599298932736, 28766348771328, 1380784741023744, 66277667569139712, 3181328043318706176, 152703746079297896448, 7329779811806299029504, 351829430966702353416192
Offset: 0

Views

Author

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

Keywords

Comments

The initial terms coincide with those of A170768, 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 1176. - Vincenzo Librandi, Dec 08 2012

Links

Programs

  • Mathematica
    With[{num = Total[2 t^Range[49]] + t^50 + 1, den = Total[-47 t^Range[49]] + 1128t^50 + 1}, CoefficientList[Series[num/den, {t, 0, 200}], t]] (* Vincenzo Librandi, Dec 08 2012 *)

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)/(1128*t^50 - 47*t^49 - 47*t^48 - 47*t^47 - 47*t^46 - 47*t^45 - 47*t^44 - 47*t^43 - 47*t^42 - 47*t^41 - 47*t^40 - 47*t^39 - 47*t^38 - 47*t^37 - 47*t^36 - 47*t^35 - 47*t^34 - 47*t^33 - 47*t^32 - 47*t^31 - 47*t^30 - 47*t^29 - 47*t^28 - 47*t^27 - 47*t^26 - 47*t^25 - 47*t^24 - 47*t^23 - 47*t^22 - 47*t^21 - 47*t^20 - 47*t^19 - 47*t^18 - 47*t^17 - 47*t^16 - 47*t^15 - 47*t^14 - 47*t^13 - 47*t^12 - 47*t^11 - 47*t^10 - 47*t^9 - 47*t^8 - 47*t^7 - 47*t^6 - 47*t^5 - 47*t^4 - 47*t^3 - 47*t^2 - 47*t + 1).

A162914 Number of reduced words of length n in Coxeter group on 49 generators S_i with relations (S_i)^2 = (S_i S_j)^3 = I.

Original entry on oeis.org

1, 49, 2352, 111720, 5306112, 251985048, 11966664360, 568291227840, 26987881799256, 1281641734875432, 60864559478706816, 2890429126368804888, 137265111357893562792, 6518655179668349992512, 309567849623689435185624
Offset: 0

Views

Author

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

Keywords

Comments

The initial terms coincide with those of A170768, 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)/(1128*t^3 - 47*t^2 - 47*t + 1)

A164694 Number of reduced words of length n in Coxeter group on 49 generators S_i with relations (S_i)^2 = (S_i S_j)^7 = I.

Original entry on oeis.org

1, 49, 2352, 112896, 5419008, 260112384, 12485394432, 599298931560, 28766348658432, 1380784732896408, 66277667049027840, 3181328012113348608, 152703744281921323008, 7329779711155291815936, 351829425445361287501224
Offset: 0

Views

Author

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

Keywords

Comments

The initial terms coincide with those of A170768, although the two sequences are eventually different.
Computed with MAGMA using commands similar to those used to compute A154638.

Links

Formula

G.f.: (t^7 + 2*t^6 + 2*t^5 + 2*t^4 + 2*t^3 + 2*t^2 + 2*t + 1)/(1128*t^7 - 47*t^6 - 47*t^5 - 47*t^4 - 47*t^3 - 47*t^2 - 47*t + 1).

A165181 Number of reduced words of length n in Coxeter group on 49 generators S_i with relations (S_i)^2 = (S_i S_j)^8 = I.

Original entry on oeis.org

1, 49, 2352, 112896, 5419008, 260112384, 12485394432, 599298932736, 28766348770152, 1380784740910848, 66277667561012376, 3181328042798594304, 152703746048092538880, 7329779810008922456064, 351829430866051346202624
Offset: 0

Views

Author

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

Keywords

Comments

The initial terms coincide with those of A170768, although the two sequences are eventually different.
Computed with MAGMA using commands similar to those used to compute A154638.

Links

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)/(1128*t^8 -
47*t^7 - 47*t^6 - 47*t^5 - 47*t^4 - 47*t^3 - 47*t^2 - 47*t + 1)

A165709 Number of reduced words of length n in Coxeter group on 49 generators S_i with relations (S_i)^2 = (S_i S_j)^9 = I.

Original entry on oeis.org

1, 49, 2352, 112896, 5419008, 260112384, 12485394432, 599298932736, 28766348771328, 1380784741022568, 66277667569026816, 3181328043310578840, 152703746078777784576, 7329779811775093671936, 351829430964904976842752
Offset: 0

Views

Author

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

Keywords

Comments

The initial terms coincide with those of A170768, 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^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)/(1128*t^9 - 47*t^8 - 47*t^7 - 47*t^6 - 47*t^5 - 47*t^4 - 47*t^3 -
47*t^2 - 47*t + 1)

A168870 Number of reduced words of length n in Coxeter group on 49 generators S_i with relations (S_i)^2 = (S_i S_j)^20 = I.

Original entry on oeis.org

1, 49, 2352, 112896, 5419008, 260112384, 12485394432, 599298932736, 28766348771328, 1380784741023744, 66277667569139712, 3181328043318706176, 152703746079297896448, 7329779811806299029504, 351829430966702353416192
Offset: 0

Views

Author

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

Keywords

Comments

The initial terms coincide with those of A170768, although the two sequences are eventually different.
First disagreement at index 20: a(20) = 4303081683335896105218435698391912, A170768(20) = 4303081683335896105218435698393088. - Klaus Brockhaus, Apr 04 2011
Computed with MAGMA using commands similar to those used to compute A154638.

Links

Crossrefs

Cf. A170768 (G.f.: (1+x)/(1-48*x)).

Formula

G.f.: (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)/(1128*t^20 - 47*t^19 - 47*t^18 - 47*t^17 - 47*t^16 - 47*t^15 - 47*t^14 - 47*t^13 - 47*t^12 - 47*t^11 - 47*t^10 - 47*t^9 - 47*t^8 - 47*t^7 - 47*t^6 - 47*t^5 - 47*t^4 - 47*t^3 - 47*t^2 - 47*t + 1).
Previous Showing 11-20 of 49 results. Next

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