A003953 -id:A003953 - cp's OEIS frontend

A165264 Number of reduced words of length n in Coxeter group on 11 generators S_i with relations (S_i)^2 = (S_i S_j)^9 = I.

1, 11, 110, 1100, 11000, 110000, 1100000, 11000000, 110000000, 1099999945, 10999998900, 109999983555, 1099999781100, 10999997266500, 109999967220000, 1099999617750000, 10999995633000000, 109999950885000000

Offset: 0

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

nonn

The initial terms coincide with those of A003953, 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 (9, 9, 9, 9, 9, 9, 9, 9, -45).

With[{num=Total[2t^Range[8]]+t^9+1,den=Total[-9 t^Range[8]]+45t^9+1}, CoefficientList[Series[num/den,{t,0,30}],t]] (* Harvey P. Dale, Oct 22 2011 *)

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)/(45*t^9 - 9*t^8 - 9*t^7 - 9*t^6 - 9*t^5 - 9*t^4 - 9*t^3 - 9*t^2 - 9*t
+ 1)

A168880 Number of reduced words of length n in Coxeter group on 11 generators S_i with relations (S_i)^2 = (S_i S_j)^21 = I.

Original entry on oeis.org

1, 11, 110, 1100, 11000, 110000, 1100000, 11000000, 110000000, 1100000000, 11000000000, 110000000000, 1100000000000, 11000000000000, 110000000000000, 1100000000000000, 11000000000000000, 110000000000000000

Offset: 0

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

nonn

The initial terms coincide with those of A003953, although the two sequences are eventually different.
First disagreement at index 21: a(21) = 1099999999999999999945, A003953(21) = 1100000000000000000000. - Klaus Brockhaus, Apr 05 2011
Computed with MAGMA using commands similar to those used to compute A154638.

Index entries for linear recurrences with constant coefficients, signature (9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, -45).

Cf. A003953 (G.f.: (1+x)/(1-10*x)).

With[{num=Total[2t^Range[20]]+t^21+1,den=Total[-9 t^Range[20]]+ 45t^21+ 1},CoefficientList[Series[num/den,{t,0,30}],t]] (* Harvey P. Dale, Feb 19 2013 *)

G.f.: (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)/(45*t^21 - 9*t^20 - 9*t^19 - 9*t^18 - 9*t^17 - 9*t^16 - 9*t^15 - 9*t^14 - 9*t^13 - 9*t^12 - 9*t^11 - 9*t^10 - 9*t^9 - 9*t^8 - 9*t^7 - 9*t^6 - 9*t^5 - 9*t^4 - 9*t^3 - 9*t^2 - 9*t + 1).

A168928 Number of reduced words of length n in Coxeter group on 11 generators S_i with relations (S_i)^2 = (S_i S_j)^22 = I.

Original entry on oeis.org

1, 11, 110, 1100, 11000, 110000, 1100000, 11000000, 110000000, 1100000000, 11000000000, 110000000000, 1100000000000, 11000000000000, 110000000000000, 1100000000000000, 11000000000000000, 110000000000000000

Offset: 0

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

nonn

The initial terms coincide with those of A003953, although the two sequences are eventually different.
First disagreement at index 22: a(22) = 10999999999999999999945, A003953(22) = 11000000000000000000000. - Klaus Brockhaus, Apr 09 2011
Computed with MAGMA using commands similar to those used to compute A154638.

Index entries for linear recurrences with constant coefficients, signature (9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, -45).

Cf. A003953 (G.f.: (1+x)/(1-10*x)).

coxG[{22,45,-9}] (* The coxG program is at A169452 *) (* Harvey P. Dale, Jun 23 2018 *)

G.f.: (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)/(45*t^22 - 9*t^21 - 9*t^20 - 9*t^19 - 9*t^18 - 9*t^17 - 9*t^16 - 9*t^15 - 9*t^14 - 9*t^13 - 9*t^12 - 9*t^11 - 9*t^10 - 9*t^9 - 9*t^8 - 9*t^7 - 9*t^6 - 9*t^5 - 9*t^4 - 9*t^3 - 9*t^2 - 9*t + 1).

A168976 Number of reduced words of length n in Coxeter group on 11 generators S_i with relations (S_i)^2 = (S_i S_j)^23 = I.

Original entry on oeis.org

1, 11, 110, 1100, 11000, 110000, 1100000, 11000000, 110000000, 1100000000, 11000000000, 110000000000, 1100000000000, 11000000000000, 110000000000000, 1100000000000000, 11000000000000000, 110000000000000000

Offset: 0

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

nonn

The initial terms coincide with those of A003953, although the two sequences are eventually different.
First disagreement at index 23: a(23) = 109999999999999999999945, A003953(23) = 110000000000000000000000. - Klaus Brockhaus, Apr 19 2011
Computed with MAGMA using commands similar to those used to compute A154638.

Index entries for linear recurrences with constant coefficients, signature (9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, -45).

Cf. A003953 (G.f.: (1+x)/(1-10*x)).

G.f.: (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)/(45*t^23 - 9*t^22 - 9*t^21 - 9*t^20 - 9*t^19 - 9*t^18 - 9*t^17 - 9*t^16 - 9*t^15 - 9*t^14 - 9*t^13 - 9*t^12 - 9*t^11 - 9*t^10 - 9*t^9 - 9*t^8 - 9*t^7 - 9*t^6 - 9*t^5 - 9*t^4 - 9*t^3 - 9*t^2 - 9*t + 1).

A169024 Number of reduced words of length n in Coxeter group on 11 generators S_i with relations (S_i)^2 = (S_i S_j)^24 = I.

Original entry on oeis.org

1, 11, 110, 1100, 11000, 110000, 1100000, 11000000, 110000000, 1100000000, 11000000000, 110000000000, 1100000000000, 11000000000000, 110000000000000, 1100000000000000, 11000000000000000, 110000000000000000

Offset: 0

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

nonn

The initial terms coincide with those of A003953, although the two sequences are eventually different.
First disagreement at index 24: a(24) = 1099999999999999999999945, A003953(24) = 1100000000000000000000000. - Klaus Brockhaus, Apr 20 2011
Computed with MAGMA using commands similar to those used to compute A154638.

Index entries for linear recurrences with constant coefficients, signature (9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, -45).

Cf. A003953 (G.f.: (1+x)/(1-10*x)).

G.f.: (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)/(45*t^24 - 9*t^23 - 9*t^22 - 9*t^21 - 9*t^20 - 9*t^19 - 9*t^18 - 9*t^17 - 9*t^16 - 9*t^15 - 9*t^14 - 9*t^13 - 9*t^12 - 9*t^11 - 9*t^10 - 9*t^9 - 9*t^8 - 9*t^7 - 9*t^6 - 9*t^5 - 9*t^4 - 9*t^3 - 9*t^2 - 9*t + 1).

A169072 Number of reduced words of length n in Coxeter group on 11 generators S_i with relations (S_i)^2 = (S_i S_j)^25 = I.

Original entry on oeis.org

1, 11, 110, 1100, 11000, 110000, 1100000, 11000000, 110000000, 1100000000, 11000000000, 110000000000, 1100000000000, 11000000000000, 110000000000000, 1100000000000000, 11000000000000000, 110000000000000000

Offset: 0

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

nonn

The initial terms coincide with those of A003953, although the two sequences are eventually different.
First disagreement at index 25: a(25) = 10999999999999999999999945, A003953(25) = 11000000000000000000000000. - Klaus Brockhaus, Apr 25 2011
Computed with MAGMA using commands similar to those used to compute A154638.

Index entries for linear recurrences with constant coefficients, signature (9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, -45).

Cf. A003953 (G.f.: (1+x)/(1-10*x)).

coxG[{25,45,-9}] (* The coxG program is at A169452 *) (* Harvey P. Dale, Feb 19 2023 *)

G.f.: (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)/(45*t^25 - 9*t^24 - 9*t^23 - 9*t^22 - 9*t^21 - 9*t^20 - 9*t^19 - 9*t^18 - 9*t^17 - 9*t^16 - 9*t^15 - 9*t^14 - 9*t^13 - 9*t^12 - 9*t^11 - 9*t^10 - 9*t^9 - 9*t^8 - 9*t^7 - 9*t^6 - 9*t^5 - 9*t^4 - 9*t^3 - 9*t^2 - 9*t + 1).

A169120 Number of reduced words of length n in Coxeter group on 11 generators S_i with relations (S_i)^2 = (S_i S_j)^26 = I.

Original entry on oeis.org

1, 11, 110, 1100, 11000, 110000, 1100000, 11000000, 110000000, 1100000000, 11000000000, 110000000000, 1100000000000, 11000000000000, 110000000000000, 1100000000000000, 11000000000000000, 110000000000000000

Offset: 0

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

nonn

The initial terms coincide with those of A003953, although the two sequences are eventually different.
First disagreement at index 26: a(26) = 109999999999999999999999945, A003953(26) = 110000000000000000000000000. - Klaus Brockhaus, Apr 30 2011
Computed with MAGMA using commands similar to those used to compute A154638.

Index entries for linear recurrences with constant coefficients, signature (9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, -45).

Cf. A003953 (G.f.: (1+x)/(1-10*x)).

coxG[{26,45,-9}] (* The coxG program is at A169452 *) (* Harvey P. Dale, Apr 29 2019 *)

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)/(45*t^26 - 9*t^25 - 9*t^24 - 9*t^23 - 9*t^22 - 9*t^21 - 9*t^20 - 9*t^19 - 9*t^18 - 9*t^17 - 9*t^16 - 9*t^15 - 9*t^14 - 9*t^13 - 9*t^12 - 9*t^11 - 9*t^10 - 9*t^9 - 9*t^8 - 9*t^7 - 9*t^6 - 9*t^5 - 9*t^4 - 9*t^3 - 9*t^2 - 9*t + 1).

A169168 Number of reduced words of length n in Coxeter group on 11 generators S_i with relations (S_i)^2 = (S_i S_j)^27 = I.

Original entry on oeis.org

1, 11, 110, 1100, 11000, 110000, 1100000, 11000000, 110000000, 1100000000, 11000000000, 110000000000, 1100000000000, 11000000000000, 110000000000000, 1100000000000000, 11000000000000000, 110000000000000000

Offset: 0

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

nonn

The initial terms coincide with those of A003953, although the two sequences are eventually different.
First disagreement at index 27: a(27) = 1099999999999999999999999945, A003953(27) = 1100000000000000000000000000. - Klaus Brockhaus, May 07 2011
Computed with MAGMA using commands similar to those used to compute A154638.

Index entries for linear recurrences with constant coefficients, signature (9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, -45).

Cf. A003953 (G.f.: (1+x)/(1-10*x)).

coxG[{27,45,-9}] (* The coxG program is at A169452 *) (* Harvey P. Dale, Oct 05 2017 *)

G.f.: (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)/(45*t^27 - 9*t^26 - 9*t^25 - 9*t^24 - 9*t^23 - 9*t^22 - 9*t^21 - 9*t^20 - 9*t^19 - 9*t^18 - 9*t^17 - 9*t^16 - 9*t^15 - 9*t^14 - 9*t^13 - 9*t^12 - 9*t^11 - 9*t^10 - 9*t^9 - 9*t^8 - 9*t^7 - 9*t^6 - 9*t^5 - 9*t^4 - 9*t^3 - 9*t^2 - 9*t + 1).

A169216 Number of reduced words of length n in Coxeter group on 11 generators S_i with relations (S_i)^2 = (S_i S_j)^28 = I.

Original entry on oeis.org

1, 11, 110, 1100, 11000, 110000, 1100000, 11000000, 110000000, 1100000000, 11000000000, 110000000000, 1100000000000, 11000000000000, 110000000000000, 1100000000000000, 11000000000000000, 110000000000000000

Offset: 0

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

nonn

The initial terms coincide with those of A003953, although the two sequences are eventually different.
First disagreement at index 28: a(28) = 10999999999999999999999999945, A003953(28) = 11000000000000000000000000000. - Klaus Brockhaus, May 24 2011
Computed with Magma using commands similar to those used to compute A154638.

Index entries for linear recurrences with constant coefficients, signature (9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, -45).

Cf. A003953 (G.f.: (1+x)/(1-10*x)).

coxG[{28,45,-9}] (* The coxG program is at A169452 *) (* Harvey P. Dale, May 29 2020 *)

G.f.: (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)/(45*t^28 - 9*t^27 - 9*t^26 - 9*t^25 - 9*t^24 - 9*t^23 - 9*t^22 - 9*t^21 - 9*t^20 - 9*t^19 - 9*t^18 - 9*t^17 - 9*t^16 - 9*t^15 - 9*t^14 - 9*t^13 - 9*t^12 - 9*t^11 - 9*t^10 - 9*t^9 - 9*t^8 - 9*t^7 - 9*t^6 - 9*t^5 - 9*t^4 - 9*t^3 - 9*t^2 - 9*t + 1).

A169264 Number of reduced words of length n in Coxeter group on 11 generators S_i with relations (S_i)^2 = (S_i S_j)^29 = I.

Original entry on oeis.org

1, 11, 110, 1100, 11000, 110000, 1100000, 11000000, 110000000, 1100000000, 11000000000, 110000000000, 1100000000000, 11000000000000, 110000000000000, 1100000000000000, 11000000000000000, 110000000000000000

Offset: 0

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

nonn

The initial terms coincide with those of A003953, although the two sequences are eventually different.
First disagreement at index 29: a(29) = 109999999999999999999999999945, A003953(29) = 110000000000000000000000000000. - Klaus Brockhaus, Jun 03 2011
Computed with Magma using commands similar to those used to compute A154638.

Index entries for linear recurrences with constant coefficients, signature (9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, -45).

Cf. A003953 (G.f.: (1+x)/(1-10*x)).

coxG[{29,45,-9}] (* The coxG program is at A169452 *) (* Harvey P. Dale, Apr 29 2015 *)

G.f.: (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)/(45*t^29 - 9*t^28 - 9*t^27 - 9*t^26 - 9*t^25 - 9*t^24 - 9*t^23 - 9*t^22 - 9*t^21 - 9*t^20 - 9*t^19 - 9*t^18 - 9*t^17 - 9*t^16 - 9*t^15 - 9*t^14 - 9*t^13 - 9*t^12 - 9*t^11 - 9*t^10 - 9*t^9 - 9*t^8 - 9*t^7 - 9*t^6 - 9*t^5 - 9*t^4 - 9*t^3 - 9*t^2 - 9*t + 1).

cp's OEIS Frontend

A165264 Number of reduced words of length n in Coxeter group on 11 generators S_i with relations (S_i)^2 = (S_i S_j)^9 = I.

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A168880 Number of reduced words of length n in Coxeter group on 11 generators S_i with relations (S_i)^2 = (S_i S_j)^21 = I.

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A168928 Number of reduced words of length n in Coxeter group on 11 generators S_i with relations (S_i)^2 = (S_i S_j)^22 = I.

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A168976 Number of reduced words of length n in Coxeter group on 11 generators S_i with relations (S_i)^2 = (S_i S_j)^23 = I.

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A169024 Number of reduced words of length n in Coxeter group on 11 generators S_i with relations (S_i)^2 = (S_i S_j)^24 = I.

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A169072 Number of reduced words of length n in Coxeter group on 11 generators S_i with relations (S_i)^2 = (S_i S_j)^25 = I.

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A169120 Number of reduced words of length n in Coxeter group on 11 generators S_i with relations (S_i)^2 = (S_i S_j)^26 = I.

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A169168 Number of reduced words of length n in Coxeter group on 11 generators S_i with relations (S_i)^2 = (S_i S_j)^27 = I.

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A169216 Number of reduced words of length n in Coxeter group on 11 generators S_i with relations (S_i)^2 = (S_i S_j)^28 = I.

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