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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A170267 Number of reduced words of length n in Coxeter group on 18 generators S_i with relations (S_i)^2 = (S_i S_j)^41 = I.

Original entry on oeis.org

1, 18, 306, 5202, 88434, 1503378, 25557426, 434476242, 7386096114, 125563633938, 2134581776946, 36287890208082, 616894133537394, 10487200270135698, 178282404592306866, 3030800878069216722, 51523614927176684274
Offset: 0

Views

Author

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

Keywords

Comments

The initial terms coincide with those of A170737, 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)/(136*t^41 - 16*t^40 - 16*t^39 - 16*t^38 - 16*t^37 - 16*t^36 - 16*t^35
- 16*t^34 - 16*t^33 - 16*t^32 - 16*t^31 - 16*t^30 - 16*t^29 - 16*t^28 -
16*t^27 - 16*t^26 - 16*t^25 - 16*t^24 - 16*t^23 - 16*t^22 - 16*t^21 -
16*t^20 - 16*t^19 - 16*t^18 - 16*t^17 - 16*t^16 - 16*t^15 - 16*t^14 -
16*t^13 - 16*t^12 - 16*t^11 - 16*t^10 - 16*t^9 - 16*t^8 - 16*t^7 -
16*t^6 - 16*t^5 - 16*t^4 - 16*t^3 - 16*t^2 - 16*t + 1)

A170315 Number of reduced words of length n in Coxeter group on 18 generators S_i with relations (S_i)^2 = (S_i S_j)^42 = I.

Original entry on oeis.org

1, 18, 306, 5202, 88434, 1503378, 25557426, 434476242, 7386096114, 125563633938, 2134581776946, 36287890208082, 616894133537394, 10487200270135698, 178282404592306866, 3030800878069216722, 51523614927176684274
Offset: 0

Views

Author

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

Keywords

Comments

The initial terms coincide with those of A170737, although the two sequences are eventually different.
Computed with MAGMA using commands similar to those used to compute A154638.

Links

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)/(136*t^42 - 16*t^41 - 16*t^40 - 16*t^39 - 16*t^38 - 16*t^37 -
16*t^36 - 16*t^35 - 16*t^34 - 16*t^33 - 16*t^32 - 16*t^31 - 16*t^30 -
16*t^29 - 16*t^28 - 16*t^27 - 16*t^26 - 16*t^25 - 16*t^24 - 16*t^23 -
16*t^22 - 16*t^21 - 16*t^20 - 16*t^19 - 16*t^18 - 16*t^17 - 16*t^16 -
16*t^15 - 16*t^14 - 16*t^13 - 16*t^12 - 16*t^11 - 16*t^10 - 16*t^9 -
16*t^8 - 16*t^7 - 16*t^6 - 16*t^5 - 16*t^4 - 16*t^3 - 16*t^2 - 16*t + 1)

A170363 Number of reduced words of length n in Coxeter group on 18 generators S_i with relations (S_i)^2 = (S_i S_j)^43 = I.

Original entry on oeis.org

1, 18, 306, 5202, 88434, 1503378, 25557426, 434476242, 7386096114, 125563633938, 2134581776946, 36287890208082, 616894133537394, 10487200270135698, 178282404592306866, 3030800878069216722, 51523614927176684274
Offset: 0

Views

Author

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

Keywords

Comments

The initial terms coincide with those of A170737, 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)/(136*t^43 - 16*t^42 - 16*t^41 - 16*t^40 - 16*t^39 -
16*t^38 - 16*t^37 - 16*t^36 - 16*t^35 - 16*t^34 - 16*t^33 - 16*t^32 -
16*t^31 - 16*t^30 - 16*t^29 - 16*t^28 - 16*t^27 - 16*t^26 - 16*t^25 -
16*t^24 - 16*t^23 - 16*t^22 - 16*t^21 - 16*t^20 - 16*t^19 - 16*t^18 -
16*t^17 - 16*t^16 - 16*t^15 - 16*t^14 - 16*t^13 - 16*t^12 - 16*t^11 -
16*t^10 - 16*t^9 - 16*t^8 - 16*t^7 - 16*t^6 - 16*t^5 - 16*t^4 - 16*t^3 -
16*t^2 - 16*t + 1)

A170411 Number of reduced words of length n in Coxeter group on 18 generators S_i with relations (S_i)^2 = (S_i S_j)^44 = I.

Original entry on oeis.org

1, 18, 306, 5202, 88434, 1503378, 25557426, 434476242, 7386096114, 125563633938, 2134581776946, 36287890208082, 616894133537394, 10487200270135698, 178282404592306866, 3030800878069216722, 51523614927176684274
Offset: 0

Views

Author

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

Keywords

Comments

The initial terms coincide with those of A170737, 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)/(136*t^44 - 16*t^43 - 16*t^42 - 16*t^41 -
16*t^40 - 16*t^39 - 16*t^38 - 16*t^37 - 16*t^36 - 16*t^35 - 16*t^34 -
16*t^33 - 16*t^32 - 16*t^31 - 16*t^30 - 16*t^29 - 16*t^28 - 16*t^27 -
16*t^26 - 16*t^25 - 16*t^24 - 16*t^23 - 16*t^22 - 16*t^21 - 16*t^20 -
16*t^19 - 16*t^18 - 16*t^17 - 16*t^16 - 16*t^15 - 16*t^14 - 16*t^13 -
16*t^12 - 16*t^11 - 16*t^10 - 16*t^9 - 16*t^8 - 16*t^7 - 16*t^6 - 16*t^5
- 16*t^4 - 16*t^3 - 16*t^2 - 16*t + 1)

A170459 Number of reduced words of length n in Coxeter group on 18 generators S_i with relations (S_i)^2 = (S_i S_j)^45 = I.

Original entry on oeis.org

1, 18, 306, 5202, 88434, 1503378, 25557426, 434476242, 7386096114, 125563633938, 2134581776946, 36287890208082, 616894133537394, 10487200270135698, 178282404592306866, 3030800878069216722, 51523614927176684274
Offset: 0

Views

Author

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

Keywords

Comments

The initial terms coincide with those of A170737, 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)/(136*t^45 - 16*t^44 - 16*t^43 -
16*t^42 - 16*t^41 - 16*t^40 - 16*t^39 - 16*t^38 - 16*t^37 - 16*t^36 -
16*t^35 - 16*t^34 - 16*t^33 - 16*t^32 - 16*t^31 - 16*t^30 - 16*t^29 -
16*t^28 - 16*t^27 - 16*t^26 - 16*t^25 - 16*t^24 - 16*t^23 - 16*t^22 -
16*t^21 - 16*t^20 - 16*t^19 - 16*t^18 - 16*t^17 - 16*t^16 - 16*t^15 -
16*t^14 - 16*t^13 - 16*t^12 - 16*t^11 - 16*t^10 - 16*t^9 - 16*t^8 -
16*t^7 - 16*t^6 - 16*t^5 - 16*t^4 - 16*t^3 - 16*t^2 - 16*t + 1)

A170507 Number of reduced words of length n in Coxeter group on 18 generators S_i with relations (S_i)^2 = (S_i S_j)^46 = I.

Original entry on oeis.org

1, 18, 306, 5202, 88434, 1503378, 25557426, 434476242, 7386096114, 125563633938, 2134581776946, 36287890208082, 616894133537394, 10487200270135698, 178282404592306866, 3030800878069216722, 51523614927176684274
Offset: 0

Views

Author

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

Keywords

Comments

The initial terms coincide with those of A170737, 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[-16 t^Range[45]]+136t^46+ 1},CoefficientList[Series[num/den,{t,0,20}],t]] (* Harvey P. Dale, Aug 23 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)/(136*t^46 - 16*t^45 -
16*t^44 - 16*t^43 - 16*t^42 - 16*t^41 - 16*t^40 - 16*t^39 - 16*t^38 -
16*t^37 - 16*t^36 - 16*t^35 - 16*t^34 - 16*t^33 - 16*t^32 - 16*t^31 -
16*t^30 - 16*t^29 - 16*t^28 - 16*t^27 - 16*t^26 - 16*t^25 - 16*t^24 -
16*t^23 - 16*t^22 - 16*t^21 - 16*t^20 - 16*t^19 - 16*t^18 - 16*t^17 -
16*t^16 - 16*t^15 - 16*t^14 - 16*t^13 - 16*t^12 - 16*t^11 - 16*t^10 -
16*t^9 - 16*t^8 - 16*t^7 - 16*t^6 - 16*t^5 - 16*t^4 - 16*t^3 - 16*t^2 -
16*t + 1)

A170555 Number of reduced words of length n in Coxeter group on 18 generators S_i with relations (S_i)^2 = (S_i S_j)^47 = I.

Original entry on oeis.org

1, 18, 306, 5202, 88434, 1503378, 25557426, 434476242, 7386096114, 125563633938, 2134581776946, 36287890208082, 616894133537394, 10487200270135698, 178282404592306866, 3030800878069216722, 51523614927176684274
Offset: 0

Views

Author

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

Keywords

Comments

The initial terms coincide with those of A170737, 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)/(136*t^47 -
16*t^46 - 16*t^45 - 16*t^44 - 16*t^43 - 16*t^42 - 16*t^41 - 16*t^40 -
16*t^39 - 16*t^38 - 16*t^37 - 16*t^36 - 16*t^35 - 16*t^34 - 16*t^33 -
16*t^32 - 16*t^31 - 16*t^30 - 16*t^29 - 16*t^28 - 16*t^27 - 16*t^26 -
16*t^25 - 16*t^24 - 16*t^23 - 16*t^22 - 16*t^21 - 16*t^20 - 16*t^19 -
16*t^18 - 16*t^17 - 16*t^16 - 16*t^15 - 16*t^14 - 16*t^13 - 16*t^12 -
16*t^11 - 16*t^10 - 16*t^9 - 16*t^8 - 16*t^7 - 16*t^6 - 16*t^5 - 16*t^4
- 16*t^3 - 16*t^2 - 16*t + 1)

A170603 Number of reduced words of length n in Coxeter group on 18 generators S_i with relations (S_i)^2 = (S_i S_j)^48 = I.

Original entry on oeis.org

1, 18, 306, 5202, 88434, 1503378, 25557426, 434476242, 7386096114, 125563633938, 2134581776946, 36287890208082, 616894133537394, 10487200270135698, 178282404592306866, 3030800878069216722, 51523614927176684274
Offset: 0

Views

Author

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

Keywords

Comments

The initial terms coincide with those of A170737, 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)/(136*t^48 - 16*t^47 - 16*t^46 - 16*t^45 - 16*t^44 - 16*t^43 - 16*t^42
- 16*t^41 - 16*t^40 - 16*t^39 - 16*t^38 - 16*t^37 - 16*t^36 - 16*t^35 -
16*t^34 - 16*t^33 - 16*t^32 - 16*t^31 - 16*t^30 - 16*t^29 - 16*t^28 -
16*t^27 - 16*t^26 - 16*t^25 - 16*t^24 - 16*t^23 - 16*t^22 - 16*t^21 -
16*t^20 - 16*t^19 - 16*t^18 - 16*t^17 - 16*t^16 - 16*t^15 - 16*t^14 -
16*t^13 - 16*t^12 - 16*t^11 - 16*t^10 - 16*t^9 - 16*t^8 - 16*t^7 -
16*t^6 - 16*t^5 - 16*t^4 - 16*t^3 - 16*t^2 - 16*t + 1)

A170651 Number of reduced words of length n in Coxeter group on 18 generators S_i with relations (S_i)^2 = (S_i S_j)^49 = I.

Original entry on oeis.org

1, 18, 306, 5202, 88434, 1503378, 25557426, 434476242, 7386096114, 125563633938, 2134581776946, 36287890208082, 616894133537394, 10487200270135698, 178282404592306866, 3030800878069216722, 51523614927176684274
Offset: 0

Views

Author

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

Keywords

Comments

The initial terms coincide with those of A170737, although the two sequences are eventually different.
Computed with MAGMA using commands similar to those used to compute A154638.

Links

Programs

  • Mathematica
    coxG[{49, 136, -16}] (* The coxG program is at A169452 *) (* Harvey P. Dale, Oct 01 2018 *)

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)/(136*t^49 - 16*t^48 - 16*t^47 - 16*t^46 - 16*t^45 - 16*t^44 - 16*t^43
- 16*t^42 - 16*t^41 - 16*t^40 - 16*t^39 - 16*t^38 - 16*t^37 - 16*t^36 -
16*t^35 - 16*t^34 - 16*t^33 - 16*t^32 - 16*t^31 - 16*t^30 - 16*t^29 -
16*t^28 - 16*t^27 - 16*t^26 - 16*t^25 - 16*t^24 - 16*t^23 - 16*t^22 -
16*t^21 - 16*t^20 - 16*t^19 - 16*t^18 - 16*t^17 - 16*t^16 - 16*t^15 -
16*t^14 - 16*t^13 - 16*t^12 - 16*t^11 - 16*t^10 - 16*t^9 - 16*t^8 -
16*t^7 - 16*t^6 - 16*t^5 - 16*t^4 - 16*t^3 - 16*t^2 - 16*t + 1)
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