A170739 -id:A170739 - cp's OEIS frontend

A168745 Number of reduced words of length n in Coxeter group on 20 generators S_i with relations (S_i)^2 = (S_i S_j)^18 = I.

1, 20, 380, 7220, 137180, 2606420, 49521980, 940917620, 17877434780, 339671260820, 6453753955580, 122621325156020, 2329805177964380, 44266298381323220, 841059669245141180, 15980133715657682420

Offset: 0

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

The initial terms coincide with those of A170739, although the two sequences are eventually different.
First disagreement at index 18: a(18) = 109607737155696043718590, A170739(18) = 109607737155696043718780. - Klaus Brockhaus, Mar 27 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 (18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, -171).

Cf. A170739 (G.f.: (1+x)/(1-19*x)).

coxG[{18,171,-18}] (* The coxG program is at A169452 *) (* Harvey P. Dale, Oct 01 2015 *)
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)/(171*t^18 - 18*t^17 - 18*t^16 - 18*t^15 - 18*t^14 - 18*t^13 - 18*t^12 - 18*t^11 - 18*t^10 - 18*t^9 - 18*t^8 - 18*t^7 - 18*t^6 - 18*t^5 - 18*t^4 - 18*t^3 - 18*t^2 - 18*t + 1), {t, 0, 50}], t] (* G. C. Greubel, Aug 10 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)/(171*t^18 - 18*t^17 - 18*t^16 - 18*t^15 - 18*t^14 - 18*t^13 -18*t^12 - 18*t^11 - 18*t^10 - 18*t^9 - 18*t^8 - 18*t^7 - 18*t^6 - 18*t^5- 18*t^4 - 18*t^3 - 18*t^2 - 18*t + 1).

A168793 Number of reduced words of length n in Coxeter group on 20 generators S_i with relations (S_i)^2 = (S_i S_j)^19 = I.

Original entry on oeis.org

1, 20, 380, 7220, 137180, 2606420, 49521980, 940917620, 17877434780, 339671260820, 6453753955580, 122621325156020, 2329805177964380, 44266298381323220, 841059669245141180, 15980133715657682420

Offset: 0

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

nonn

The initial terms coincide with those of A170739, although the two sequences are eventually different.
First disagreement at index 19: a(19) = 2082547005958224830656630, A170739(19) = 2082547005958224830656820. - Klaus Brockhaus, Mar 30 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 (18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, -171).

Cf. A170739 (G.f.: (1+x)/(1-19*x)).

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)/(171*t^19 - 18*t^18 - 18*t^17 - 18*t^16 - 18*t^15 - 18*t^14 - 18*t^13 - 18*t^12 - 18*t^11 - 18*t^10 - 18*t^9 - 18*t^8 - 18*t^7 - 18*t^6 - 18*t^5 - 18*t^4 - 18*t^3 - 18*t^2 - 18*t + 1), {t, 0, 50}], t] (* G. C. Greubel, Aug 15 2016 *)

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)/(171*t^19 - 18*t^18 - 18*t^17 - 18*t^16 - 18*t^15 - 18*t^14 - 18*t^13 - 18*t^12 - 18*t^11 - 18*t^10 - 18*t^9 - 18*t^8 - 18*t^7 - 18*t^6 - 18*t^5 - 18*t^4 - 18*t^3 - 18*t^2 - 18*t + 1).

A170365 Number of reduced words of length n in Coxeter group on 20 generators S_i with relations (S_i)^2 = (S_i S_j)^43 = I.

Original entry on oeis.org

1, 20, 380, 7220, 137180, 2606420, 49521980, 940917620, 17877434780, 339671260820, 6453753955580, 122621325156020, 2329805177964380, 44266298381323220, 841059669245141180, 15980133715657682420

Offset: 0

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

nonn

The initial terms coincide with those of A170739, although the two sequences are eventually different.

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 (18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, -171).

With[{num=Total[2t^Range[42]]+t^43+1,den=Total[-18 t^Range[42]]+ 171t^43+ 1}, CoefficientList[Series[num/den,{t,0,30}],t]] (* Harvey P. Dale, Jan 14 2012 *)

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)/(171*t^43 - 18*t^42 - 18*t^41 - 18*t^40 - 18*t^39 - 18*t^38 - 18*t^37 - 18*t^36 - 18*t^35 - 18*t^34 - 18*t^33 - 18*t^32 - 18*t^31 - 18*t^30 - 18*t^29 - 18*t^28 - 18*t^27 - 18*t^26 - 18*t^25 - 18*t^24 - 18*t^23 - 18*t^22 - 18*t^21 - 18*t^20 - 18*t^19 - 18*t^18 - 18*t^17 - 18*t^16 - 18*t^15 - 18*t^14 - 18*t^13 - 18*t^12 - 18*t^11 - 18*t^10 - 18*t^9 - 18*t^8 - 18*t^7 - 18*t^6 - 18*t^5 - 18*t^4 - 18*t^3 - 18*t^2 - 18*t + 1)

A170701 Number of reduced words of length n in Coxeter group on 20 generators S_i with relations (S_i)^2 = (S_i S_j)^50 = I.

Original entry on oeis.org

1, 20, 380, 7220, 137180, 2606420, 49521980, 940917620, 17877434780, 339671260820, 6453753955580, 122621325156020, 2329805177964380, 44266298381323220, 841059669245141180, 15980133715657682420

Offset: 0

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

nonn

The initial terms coincide with those of A170739, 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 190.  - Vincenzo Librandi, Dec 08 2012

Vincenzo Librandi, Table of n, a(n) for n = 0..200
Index entries for linear recurrences with constant coefficients, signature (18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, -171).

With[{num = Total[2 t^Range[49]] + t^50 + 1, den = Total[-18 t^Range[49]] + 171t^50 + 1}, CoefficientList[Series[num/den, {t, 0, 20}], t]] (* Vincenzo Librandi, Dec 08 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)/(171*t^50 - 18*t^49 - 18*t^48 - 18*t^47 - 18*t^46 - 18*t^45 -
18*t^44 - 18*t^43 - 18*t^42 - 18*t^41 - 18*t^40 - 18*t^39 - 18*t^38 -
18*t^37 - 18*t^36 - 18*t^35 - 18*t^34 - 18*t^33 - 18*t^32 - 18*t^31 -
18*t^30 - 18*t^29 - 18*t^28 - 18*t^27 - 18*t^26 - 18*t^25 - 18*t^24 -
18*t^23 - 18*t^22 - 18*t^21 - 18*t^20 - 18*t^19 - 18*t^18 - 18*t^17 -
18*t^16 - 18*t^15 - 18*t^14 - 18*t^13 - 18*t^12 - 18*t^11 - 18*t^10 -
18*t^9 - 18*t^8 - 18*t^7 - 18*t^6 - 18*t^5 - 18*t^4 - 18*t^3 - 18*t^2 -
18*t + 1)

A162806 Number of reduced words of length n in Coxeter group on 20 generators S_i with relations (S_i)^2 = (S_i S_j)^3 = I.

Original entry on oeis.org

1, 20, 380, 7030, 129960, 2400840, 44352270, 819332820, 15135787980, 279607936230, 5165281123560, 95419783331640, 1762718203098270, 32563220683609620, 601550117011031580, 11112615265773737430

Offset: 0

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

nonn

The initial terms coincide with those of A170739, 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 (18, 18, -171).

coxG[{3,171,-18}] (* The coxG program is at A169452 *) (* Harvey P. Dale, Jul 10 2020 *)

G.f.: (t^3 + 2*t^2 + 2*t + 1)/(171*t^3 - 18*t^2 - 18*t + 1)

A163124 Number of reduced words of length n in Coxeter group on 20 generators S_i with relations (S_i)^2 = (S_i S_j)^4 = I.

Original entry on oeis.org

1, 20, 380, 7220, 136990, 2599200, 49316400, 935712000, 17753871510, 336855735180, 6391382632020, 121267853544780, 2300893742387430, 43656351283440360, 828320305398630840, 15716259104684097960

Offset: 0

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

nonn

The initial terms coincide with those of A170739, 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 (18, 18, 18, -171).

coxG[{4,171,-18}] (* The coxG program is at A169452 *) (* Harvey P. Dale, Dec 14 2015 *)

G.f.: (t^4 + 2*t^3 + 2*t^2 + 2*t + 1)/(171*t^4 - 18*t^3 - 18*t^2 - 18*t + 1)

A163969 Number of reduced words of length n in Coxeter group on 20 generators S_i with relations (S_i)^2 = (S_i S_j)^6 = I.

Original entry on oeis.org

1, 20, 380, 7220, 137180, 2606420, 49521790, 940910400, 17877229200, 339666055200, 6453630356400, 122618507616000, 2329742730783510, 44264942521047180, 841030689999256020, 15979521970107624780

Offset: 0

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

The initial terms coincide with those of A170739, 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 (18, 18, 18, 18, 18, -171).

coxG[{6,171,-18}] (* The coxG program is at A169452 *) (* Harvey P. Dale, May 21 2015 *)
CoefficientList[Series[(t^6 + 2*t^5 + 2*t^4 + 2*t^3 + 2*t^2 + 2*t + 1)/(171*t^6 - 18*t^5 - 18*t^4 - 18*t^3 - 18*t^2 - 18*t + 1), {t,0,50}], t] (* G. C. Greubel, Aug 23 2017 *)

t='t+O('t^50); Vec((t^6 + 2*t^5 + 2*t^4 + 2*t^3 + 2*t^2 + 2*t + 1)/(171*t^6 - 18*t^5 - 18*t^4 - 18*t^3 - 18*t^2 - 18*t + 1)) \\ G. C. Greubel, Aug 23 2017

G.f.: (t^6 + 2*t^5 + 2*t^4 + 2*t^3 + 2*t^2 + 2*t + 1)/(171*t^6 - 18*t^5 - 18*t^4 - 18*t^3 - 18*t^2 - 18*t + 1).

A164633 Number of reduced words of length n in Coxeter group on 20 generators S_i with relations (S_i)^2 = (S_i S_j)^7 = I.

Original entry on oeis.org

1, 20, 380, 7220, 137180, 2606420, 49521980, 940917430, 17877427560, 339671055240, 6453748749960, 122621201556840, 2329802360424360, 44266235934106440, 841058313382886670, 15980104736337918420

Offset: 0

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

nonn

The initial terms coincide with those of A170739, 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 (18,18,18,18,18,18,-171).

G.f.: (t^7 + 2*t^6 + 2*t^5 + 2*t^4 + 2*t^3 + 2*t^2 + 2*t + 1)/(171*t^7 - 18*t^6 - 18*t^5 - 18*t^4 - 18*t^3 - 18*t^2 - 18*t + 1).

A164911 Number of reduced words of length n in Coxeter group on 20 generators S_i with relations (S_i)^2 = (S_i S_j)^8 = I.

Original entry on oeis.org

1, 20, 380, 7220, 137180, 2606420, 49521980, 940917620, 17877434590, 339671253600, 6453753750000, 122621319950400, 2329805054365200, 44266295563783200, 841059606797924400, 15980132359795392000

Offset: 0

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

nonn

The initial terms coincide with those of A170739, 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 (18, 18, 18, 18, 18, 18, 18, -171).

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)/(171*t^8 -

18*t^7 - 18*t^6 - 18*t^5 - 18*t^4 - 18*t^3 - 18*t^2 - 18*t + 1)

A165348 Number of reduced words of length n in Coxeter group on 20 generators S_i with relations (S_i)^2 = (S_i S_j)^9 = I.

Original entry on oeis.org

1, 20, 380, 7220, 137180, 2606420, 49521980, 940917620, 17877434780, 339671260630, 6453753948360, 122621324950440, 2329805172758760, 44266298257724040, 841059666427601160, 15980133653210465640

Offset: 0

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

nonn

The initial terms coincide with those of A170739, 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 (18, 18, 18, 18, 18, 18, 18, 18, -171).

coxG[{9,171,-18}] (* The coxG program is at A169452 *) (* Harvey P. Dale, May 06 2018 *)

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)/(171*t^9 - 18*t^8 - 18*t^7 - 18*t^6 - 18*t^5 - 18*t^4 - 18*t^3 -
18*t^2 - 18*t + 1)

cp's OEIS Frontend

A168745 Number of reduced words of length n in Coxeter group on 20 generators S_i with relations (S_i)^2 = (S_i S_j)^18 = I.

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A168793 Number of reduced words of length n in Coxeter group on 20 generators S_i with relations (S_i)^2 = (S_i S_j)^19 = I.

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A170365 Number of reduced words of length n in Coxeter group on 20 generators S_i with relations (S_i)^2 = (S_i S_j)^43 = I.

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A170701 Number of reduced words of length n in Coxeter group on 20 generators S_i with relations (S_i)^2 = (S_i S_j)^50 = I.

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A162806 Number of reduced words of length n in Coxeter group on 20 generators S_i with relations (S_i)^2 = (S_i S_j)^3 = I.

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A163124 Number of reduced words of length n in Coxeter group on 20 generators S_i with relations (S_i)^2 = (S_i S_j)^4 = I.

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A163969 Number of reduced words of length n in Coxeter group on 20 generators S_i with relations (S_i)^2 = (S_i S_j)^6 = I.

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A164633 Number of reduced words of length n in Coxeter group on 20 generators S_i with relations (S_i)^2 = (S_i S_j)^7 = I.

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A164911 Number of reduced words of length n in Coxeter group on 20 generators S_i with relations (S_i)^2 = (S_i S_j)^8 = I.

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