A170754 -id:A170754 - cp's OEIS frontend

A168712 Number of reduced words of length n in Coxeter group on 35 generators S_i with relations (S_i)^2 = (S_i S_j)^17 = I.

1, 35, 1190, 40460, 1375640, 46771760, 1590239840, 54068154560, 1838317255040, 62502786671360, 2125094746826240, 72253221392092160, 2456609527331133440, 83524723929258536960, 2839840613594790256640, 96554580862222868725760

Offset: 0

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

nonn

The initial terms coincide with those of A170754, although the two sequences are eventually different.
First disagreement at index 17: a(17) = 111617095476729636246977965, A170754(17) = 111617095476729636246978560. - Klaus Brockhaus, Mar 28 2011
Computed with MAGMA using commands similar to those used to compute A154638.

G. C. Greubel, Table of n, a(n) for n = 0..500
Index entries for linear recurrences with constant coefficients, signature (33, 33, 33, 33, 33, 33, 33, 33, 33, 33, 33, 33, 33, 33, 33, 33, -561).

Cf. A170754 (G.f.: (1+x)/(1-34*x)).

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)/(561*t^17 - 33*t^16 - 33*t^15 - 33*t^14 - 33*t^13 - 33*t^12 - 33*t^11 - 33*t^10 - 33*t^9 - 33*t^8 - 33*t^7 - 33*t^6 - 33*t^5 - 33*t^4 - 33*t^3 - 33*t^2 - 33*t + 1), {t,0,50}], t] (* G. C. Greubel, Aug 05 2016 *)
coxG[{17,561,-33}] (* The coxG program is at A169452 *) (* Harvey P. Dale, May 03 2025 *)

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)/(561*t^17 - 33*t^16 - 33*t^15 - 33*t^14 - 33*t^13 - 33*t^12 - 33*t^11 - 33*t^10 - 33*t^9 - 33*t^8 - 33*t^7 - 33*t^6 - 33*t^5 - 33*t^4 - 33*t^3 - 33*t^2 - 33*t + 1).

A168760 Number of reduced words of length n in Coxeter group on 35 generators S_i with relations (S_i)^2 = (S_i S_j)^18 = I.

Original entry on oeis.org

1, 35, 1190, 40460, 1375640, 46771760, 1590239840, 54068154560, 1838317255040, 62502786671360, 2125094746826240, 72253221392092160, 2456609527331133440, 83524723929258536960, 2839840613594790256640, 96554580862222868725760

Offset: 0

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

The initial terms coincide with those of A170754, although the two sequences are eventually different.
First disagreement at index 18: a(18) = 3794981246208807632397270445, A170754(18) = 3794981246208807632397271040. - Klaus Brockhaus, Mar 26 2011
Computed with MAGMA using commands similar to those used to compute A154638.

G. C. Greubel, Table of n, a(n) for n = 0..500
Index entries for linear recurrences with constant coefficients, signature (33, 33, 33, 33, 33, 33, 33, 33, 33, 33, 33, 33, 33, 33, 33, 33, 33, -561).

Cf. A170754 (G.f.: (1+x)/(1-34*x)).

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)/(561*t^18 - 33*t^17 - 33*t^16 - 33*t^15 - 33*t^14 - 33*t^13 - 33*t^12 - 33*t^11 - 33*t^10 - 33*t^9 - 33*t^8 - 33*t^7 - 33*t^6 - 33*t^5 - 33*t^4 - 33*t^3 - 33*t^2 - 33*t + 1), {t, 0, 50}], t] (* G. C. Greubel, Aug 11 2016 *)

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)/(561*t^18 - 33*t^17 - 33*t^16 - 33*t^15 - 33*t^14 - 33*t^13 - 33*t^12 - 33*t^11 - 33*t^10 - 33*t^9 - 33*t^8 - 33*t^7 - 33*t^6 - 33*t^5 - 33*t^4 - 33*t^3 - 33*t^2 - 33*t + 1).

A168808 Number of reduced words of length n in Coxeter group on 35 generators S_i with relations (S_i)^2 = (S_i S_j)^19 = I.

Original entry on oeis.org

1, 35, 1190, 40460, 1375640, 46771760, 1590239840, 54068154560, 1838317255040, 62502786671360, 2125094746826240, 72253221392092160, 2456609527331133440, 83524723929258536960, 2839840613594790256640, 96554580862222868725760

Offset: 0

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

nonn

The initial terms coincide with those of A170754, although the two sequences are eventually different.
First disagreement at index 19: a(19) = 129029362371099459501507214765, A170754(19) = 129029362371099459501507215360. - Klaus Brockhaus, Apr 01 2011
Computed with MAGMA using commands similar to those used to compute A154638.

Vincenzo Librandi, Table of n, a(n) for n = 0..200
Index entries for linear recurrences with constant coefficients, signature (33, 33, 33, 33, 33, 33, 33, 33, 33, 33, 33, 33, 33, 33, 33, 33, 33, 33, -561).

Cf. A170754 (G.f.: (1+x)/(1-34*x)).

With[{num=Total[2t^Range[18]]+t^19+1,den=Total[-33 t^Range[18]]+ 561t^19+ 1}, CoefficientList[Series[num/den,{t,0,30}],t]] (* Harvey P. Dale, Mar 11 2012 *)

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)/(561*t^19 - 33*t^18 - 33*t^17 - 33*t^16 - 33*t^15 - 33*t^14 - 33*t^13 - 33*t^12 - 33*t^11 - 33*t^10 - 33*t^9 - 33*t^8 - 33*t^7 - 33*t^6 - 33*t^5 - 33*t^4 - 33*t^3 - 33*t^2 - 33*t + 1).

A170716 Number of reduced words of length n in Coxeter group on 35 generators S_i with relations (S_i)^2 = (S_i S_j)^50 = I.

Original entry on oeis.org

1, 35, 1190, 40460, 1375640, 46771760, 1590239840, 54068154560, 1838317255040, 62502786671360, 2125094746826240, 72253221392092160, 2456609527331133440, 83524723929258536960, 2839840613594790256640, 96554580862222868725760

Offset: 0

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

nonn

The initial terms coincide with those of A170754, 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 595.  - Vincenzo Librandi, Dec 06 2012

Vincenzo Librandi, Table of n, a(n) for n = 0..200
Index entries for linear recurrences with constant coefficients, signature (33, 33, 33, 33, 33, 33, 33, 33, 33, 33, 33, 33, 33, 33, 33, 33, 33, 33, 33, 33, 33, 33, 33, 33, 33, 33, 33, 33, 33, 33, 33, 33, 33, 33, 33, 33, 33, 33, 33, 33, 33, 33, 33, 33, 33, 33, 33, 33, 33, -561).

With[{num=Total[2t^Range[49]]+t^50+1,den=Total[-33 t^Range[49]]+ 561t^50+ 1},CoefficientList[Series[num/den,{t,0,40}],t]] (* Harvey P. Dale, Sep 10 2012 *)

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)/(561*t^50 - 33*t^49 - 33*t^48 - 33*t^47 - 33*t^46 - 33*t^45 -
33*t^44 - 33*t^43 - 33*t^42 - 33*t^41 - 33*t^40 - 33*t^39 - 33*t^38 -
33*t^37 - 33*t^36 - 33*t^35 - 33*t^34 - 33*t^33 - 33*t^32 - 33*t^31 -
33*t^30 - 33*t^29 - 33*t^28 - 33*t^27 - 33*t^26 - 33*t^25 - 33*t^24 -
33*t^23 - 33*t^22 - 33*t^21 - 33*t^20 - 33*t^19 - 33*t^18 - 33*t^17 -
33*t^16 - 33*t^15 - 33*t^14 - 33*t^13 - 33*t^12 - 33*t^11 - 33*t^10 -
33*t^9 - 33*t^8 - 33*t^7 - 33*t^6 - 33*t^5 - 33*t^4 - 33*t^3 - 33*t^2 -
33*t + 1).

A162847 Number of reduced words of length n in Coxeter group on 35 generators S_i with relations (S_i)^2 = (S_i S_j)^3 = I.

Original entry on oeis.org

1, 35, 1190, 39865, 1335180, 44708895, 1497090210, 50130334485, 1678623324840, 56209003149915, 1882168556020830, 63024751767399345, 2110395119905763460, 70666959205286686935, 2366295806989839830490, 79235839622172041773965

Offset: 0

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

nonn

The initial terms coincide with those of A170754, although the two sequences are eventually different.

Computed with MAGMA using commands similar to those used to compute A154638.

Index entries for linear recurrences with constant coefficients, signature (33, 33, -561).

coxG[{3,561,-33}] (* The coxG program is at A169452 *) (* Harvey P. Dale, Oct 05 2016 *)

G.f.: (t^3 + 2*t^2 + 2*t + 1)/(561*t^3 - 33*t^2 - 33*t + 1).

a(n) = 33*a(n-1) + 33*a(n-2) - 561*a(n-3). - Wesley Ivan Hurt, Apr 20 2021

A164068 Number of reduced words of length n in Coxeter group on 35 generators S_i with relations (S_i)^2 = (S_i S_j)^6 = I.

Original entry on oeis.org

1, 35, 1190, 40460, 1375640, 46771760, 1590239245, 54068114100, 1838315192175, 62502693168300, 2125090773290100, 72253059281172000, 2456603097196693830, 83524474080352031265, 2839831057104956921160, 96554219846263616159415

Offset: 0

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

nonn

The initial terms coincide with those of A170754, although the two sequences are eventually different.

Computed with MAGMA using commands similar to those used to compute A154638.

Index entries for linear recurrences with constant coefficients, signature (33, 33, 33, 33, 33, -561).

CoefficientList[Series[(t^6 + 2*t^5 + 2*t^4 + 2*t^3 + 2*t^2 + 2*t + 1)/(561*t^6 - 33*t^5 - 33*t^4 - 33*t^3 - 33*t^2 - 33*t + 1), {t,0,50}], t] (* G. C. Greubel, Sep 09 2017 *)
coxG[{6,561,-33}] (* The coxG program is at A169452 *) (* Harvey P. Dale, May 27 2018 *)

t='t+O('t^50); Vec((t^6 + 2*t^5 + 2*t^4 + 2*t^3 + 2*t^2 + 2*t + 1)/(561*t^6 - 33*t^5 - 33*t^4 - 33*t^3 - 33*t^2 - 33*t + 1)) \\ G. C. Greubel, Sep 09 2017

G.f.: (t^6 + 2*t^5 + 2*t^4 + 2*t^3 + 2*t^2 + 2*t + 1)/(561*t^6 - 33*t^5 - 33*t^4 - 33*t^3 - 33*t^2 - 33*t + 1).

A164671 Number of reduced words of length n in Coxeter group on 35 generators S_i with relations (S_i)^2 = (S_i S_j)^7 = I.

Original entry on oeis.org

1, 35, 1190, 40460, 1375640, 46771760, 1590239840, 54068153965, 1838317214580, 62502784608495, 2125094653323180, 72253217418556020, 2456609365220213280, 83524717499123743920, 2839840363745848388310, 96554571305730654116385

Offset: 0

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

nonn

The initial terms coincide with those of A170754, although the two sequences are eventually different.

Computed with MAGMA using commands similar to those used to compute A154638.

Index entries for linear recurrences with constant coefficients, signature (33,33,33,33,33,33,-561).

coxG[{7,561,-33}] (* The coxG program is at A169452 *) (* Harvey P. Dale, Feb 11 2025 *)

G.f.: (t^7 + 2*t^6 + 2*t^5 + 2*t^4 + 2*t^3 + 2*t^2 + 2*t + 1)/(561*t^7 - 33*t^6 - 33*t^5 - 33*t^4 - 33*t^3 - 33*t^2 - 33*t + 1).

A165167 Number of reduced words of length n in Coxeter group on 35 generators S_i with relations (S_i)^2 = (S_i S_j)^8 = I.

Original entry on oeis.org

1, 35, 1190, 40460, 1375640, 46771760, 1590239840, 54068154560, 1838317254445, 62502786630900, 2125094744763375, 72253221298589100, 2456609523357597300, 83524723767147616800, 2839840607164655463600, 96554580612373926504000

Offset: 0

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

nonn

The initial terms coincide with those of A170754, although the two sequences are eventually different.

Computed with MAGMA using commands similar to those used to compute A154638.

Index entries for linear recurrences with constant coefficients, signature (33, 33, 33, 33, 33, 33, 33, -561).

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)/(561*t^8 -

33*t^7 - 33*t^6 - 33*t^5 - 33*t^4 - 33*t^3 - 33*t^2 - 33*t + 1)

A165650 Number of reduced words of length n in Coxeter group on 35 generators S_i with relations (S_i)^2 = (S_i S_j)^9 = I.

Original entry on oeis.org

1, 35, 1190, 40460, 1375640, 46771760, 1590239840, 54068154560, 1838317255040, 62502786670765, 2125094746785780, 72253221390029295, 2456609527237630380, 83524723925285000820, 2839840613432679336480, 96554580855792733932720

Offset: 0

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

nonn

The initial terms coincide with those of A170754, although the two sequences are eventually different.

Computed with MAGMA using commands similar to those used to compute A154638.

Index entries for linear recurrences with constant coefficients, signature (33, 33, 33, 33, 33, 33, 33, 33, -561).

coxG[{9,561,-33}] (* The coxG program is at A169452 *) (* Harvey P. Dale, Oct 14 2022 *)

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)/(561*t^9 - 33*t^8 - 33*t^7 - 33*t^6 - 33*t^5 - 33*t^4 - 33*t^3 -
33*t^2 - 33*t + 1)

A168856 Number of reduced words of length n in Coxeter group on 35 generators S_i with relations (S_i)^2 = (S_i S_j)^20 = I.

Original entry on oeis.org

1, 35, 1190, 40460, 1375640, 46771760, 1590239840, 54068154560, 1838317255040, 62502786671360, 2125094746826240, 72253221392092160, 2456609527331133440, 83524723929258536960, 2839840613594790256640, 96554580862222868725760

Offset: 0

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

nonn

The initial terms coincide with those of A170754, although the two sequences are eventually different.
First disagreement at index 20: a(20) = 4386998320617381623051245321645, A170754(20) = 4386998320617381623051245322240. - Klaus Brockhaus, Apr 04 2011
Computed with MAGMA using commands similar to those used to compute A154638.

Index entries for linear recurrences with constant coefficients, signature (33, 33, 33, 33, 33, 33, 33, 33, 33, 33, 33, 33, 33, 33, 33, 33, 33, 33, 33, -561).

Cf. A170754 (G.f.: (1+x)/(1-34*x)).

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)/(561*t^20 - 33*t^19 - 33*t^18 - 33*t^17 - 33*t^16 - 33*t^15 - 33*t^14 - 33*t^13 - 33*t^12 - 33*t^11 - 33*t^10 - 33*t^9 - 33*t^8 - 33*t^7 - 33*t^6 - 33*t^5 - 33*t^4 - 33*t^3 - 33*t^2 - 33*t + 1).

cp's OEIS Frontend

A168712 Number of reduced words of length n in Coxeter group on 35 generators S_i with relations (S_i)^2 = (S_i S_j)^17 = I.

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A168760 Number of reduced words of length n in Coxeter group on 35 generators S_i with relations (S_i)^2 = (S_i S_j)^18 = I.

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A168808 Number of reduced words of length n in Coxeter group on 35 generators S_i with relations (S_i)^2 = (S_i S_j)^19 = I.

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A170716 Number of reduced words of length n in Coxeter group on 35 generators S_i with relations (S_i)^2 = (S_i S_j)^50 = I.

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A162847 Number of reduced words of length n in Coxeter group on 35 generators S_i with relations (S_i)^2 = (S_i S_j)^3 = I.

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A164068 Number of reduced words of length n in Coxeter group on 35 generators S_i with relations (S_i)^2 = (S_i S_j)^6 = I.

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A164671 Number of reduced words of length n in Coxeter group on 35 generators S_i with relations (S_i)^2 = (S_i S_j)^7 = I.

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A165167 Number of reduced words of length n in Coxeter group on 35 generators S_i with relations (S_i)^2 = (S_i S_j)^8 = I.

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A165650 Number of reduced words of length n in Coxeter group on 35 generators S_i with relations (S_i)^2 = (S_i S_j)^9 = I.

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