A170741 -id:A170741 - cp's OEIS frontend

A168891 Number of reduced words of length n in Coxeter group on 22 generators S_i with relations (S_i)^2 = (S_i S_j)^21 = I.

1, 22, 462, 9702, 203742, 4278582, 89850222, 1886854662, 39623947902, 832102905942, 17474161024782, 366957381520422, 7706105011928862, 161828205250506102, 3398392310260628142, 71366238515473190982

Offset: 0

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

nonn

The initial terms coincide with those of A170741, although the two sequences are eventually different.
First disagreement at index 21: a(21) = 6120805447832934070018320591, A170741(21) = 6120805447832934070018320822. - 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 (20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, -210).

Cf. A170741 (G.f.: (1+x)/(1-21*x)).

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)/(210*t^21 - 20*t^20 - 20*t^19 - 20*t^18 - 20*t^17 - 20*t^16 - 20*t^15 - 20*t^14 - 20*t^13 - 20*t^12 - 20*t^11 - 20*t^10 - 20*t^9 - 20*t^8 - 20*t^7 - 20*t^6 - 20*t^5 - 20*t^4 - 20*t^3 - 20*t^2 - 20*t + 1).

A168939 Number of reduced words of length n in Coxeter group on 22 generators S_i with relations (S_i)^2 = (S_i S_j)^22 = I.

Original entry on oeis.org

1, 22, 462, 9702, 203742, 4278582, 89850222, 1886854662, 39623947902, 832102905942, 17474161024782, 366957381520422, 7706105011928862, 161828205250506102, 3398392310260628142, 71366238515473190982

Offset: 0

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

nonn

The initial terms coincide with those of A170741, although the two sequences are eventually different.
First disagreement at index 22: a(22) = 128536914404491615470384737031, A170741(22) = 128536914404491615470384737262. - 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 (20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, -210).

Cf. A170741 (G.f.: (1+x)/(1-21*x)).

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)/(210*t^22 - 20*t^21 - 20*t^20 - 20*t^19 - 20*t^18 - 20*t^17 - 20*t^16 - 20*t^15 - 20*t^14 - 20*t^13 - 20*t^12 - 20*t^11 - 20*t^10 - 20*t^9 - 20*t^8 - 20*t^7 - 20*t^6 - 20*t^5 - 20*t^4 - 20*t^3 - 20*t^2 - 20*t + 1).

A168987 Number of reduced words of length n in Coxeter group on 22 generators S_i with relations (S_i)^2 = (S_i S_j)^23 = I.

Original entry on oeis.org

1, 22, 462, 9702, 203742, 4278582, 89850222, 1886854662, 39623947902, 832102905942, 17474161024782, 366957381520422, 7706105011928862, 161828205250506102, 3398392310260628142, 71366238515473190982

Offset: 0

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

nonn

The initial terms coincide with those of A170741, although the two sequences are eventually different.
First disagreement at index 23: a(23) = 2699275202494323924878079482271, A170741(23) = 2699275202494323924878079482502. - 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 (20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, -210).

Cf. A170741 (G.f.: (1+x)/(1-21*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)/(210*t^23 - 20*t^22 - 20*t^21 - 20*t^20 - 20*t^19 - 20*t^18 - 20*t^17 - 20*t^16 - 20*t^15 - 20*t^14 - 20*t^13 - 20*t^12 - 20*t^11 - 20*t^10 - 20*t^9 - 20*t^8 - 20*t^7 - 20*t^6 - 20*t^5 - 20*t^4 - 20*t^3 - 20*t^2 - 20*t + 1).

A169035 Number of reduced words of length n in Coxeter group on 22 generators S_i with relations (S_i)^2 = (S_i S_j)^24 = I.

Original entry on oeis.org

1, 22, 462, 9702, 203742, 4278582, 89850222, 1886854662, 39623947902, 832102905942, 17474161024782, 366957381520422, 7706105011928862, 161828205250506102, 3398392310260628142, 71366238515473190982

Offset: 0

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

nonn

The initial terms coincide with those of A170741, although the two sequences are eventually different.
First disagreement at index 24: a(24) = 56684779252380802422439669132311, A170741(24) = 56684779252380802422439669132542. - 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 (20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, -210).

Cf. A170741 (G.f.: (1+x)/(1-21*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)/(210*t^24 - 20*t^23 - 20*t^22 - 20*t^21 - 20*t^20 - 20*t^19 - 20*t^18 - 20*t^17 - 20*t^16 - 20*t^15 - 20*t^14 - 20*t^13 - 20*t^12 - 20*t^11 - 20*t^10 - 20*t^9 - 20*t^8 - 20*t^7 - 20*t^6 - 20*t^5 - 20*t^4 - 20*t^3 - 20*t^2 - 20*t + 1).

A169083 Number of reduced words of length n in Coxeter group on 22 generators S_i with relations (S_i)^2 = (S_i S_j)^25 = I.

Original entry on oeis.org

1, 22, 462, 9702, 203742, 4278582, 89850222, 1886854662, 39623947902, 832102905942, 17474161024782, 366957381520422, 7706105011928862, 161828205250506102, 3398392310260628142, 71366238515473190982

Offset: 0

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

nonn

The initial terms coincide with those of A170741, although the two sequences are eventually different.
First disagreement at index 25: a(25) = 1190380364299996850871233051783151, A170741(25) = 1190380364299996850871233051783382. - 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 (20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, -210).

Cf. A170741 (G.f.: (1+x)/(1-21*x)).

coxG[{25,210,-20}] (* The coxG program is at A169452 *) (* Harvey P. Dale, Jun 12 2020 *)

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)/(210*t^25 - 20*t^24 - 20*t^23 - 20*t^22 - 20*t^21 - 20*t^20 - 20*t^19 - 20*t^18 - 20*t^17 - 20*t^16 - 20*t^15 - 20*t^14 - 20*t^13 - 20*t^12 - 20*t^11 - 20*t^10 - 20*t^9 - 20*t^8 - 20*t^7 - 20*t^6 - 20*t^5 - 20*t^4 - 20*t^3 - 20*t^2 - 20*t + 1).

A169131 Number of reduced words of length n in Coxeter group on 22 generators S_i with relations (S_i)^2 = (S_i S_j)^26 = I.

Original entry on oeis.org

1, 22, 462, 9702, 203742, 4278582, 89850222, 1886854662, 39623947902, 832102905942, 17474161024782, 366957381520422, 7706105011928862, 161828205250506102, 3398392310260628142, 71366238515473190982

Offset: 0

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

nonn

The initial terms coincide with those of A170741, although the two sequences are eventually different.
First disagreement at index 26: a(26) = 24997987650299933868295894087450791, A170741(26) = 24997987650299933868295894087451022. - 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 (20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, -210).

Cf. A170741 (G.f.: (1+x)/(1-21*x)).

coxG[{26,210,-20}] (* The coxG program is at A169452 *) (* Harvey P. Dale, May 15 2025 *)

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)/(210*t^26 - 20*t^25 - 20*t^24 - 20*t^23 - 20*t^22 - 20*t^21 - 20*t^20 - 20*t^19 - 20*t^18 - 20*t^17 - 20*t^16 - 20*t^15 - 20*t^14 - 20*t^13 - 20*t^12 - 20*t^11 - 20*t^10 - 20*t^9 - 20*t^8 - 20*t^7 - 20*t^6 - 20*t^5 - 20*t^4 - 20*t^3 - 20*t^2 - 20*t + 1).

A169179 Number of reduced words of length n in Coxeter group on 22 generators S_i with relations (S_i)^2 = (S_i S_j)^27 = I.

Original entry on oeis.org

1, 22, 462, 9702, 203742, 4278582, 89850222, 1886854662, 39623947902, 832102905942, 17474161024782, 366957381520422, 7706105011928862, 161828205250506102, 3398392310260628142, 71366238515473190982

Offset: 0

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

nonn

The initial terms coincide with those of A170741, although the two sequences are eventually different.
First disagreement at index 27: a(27) = 524957740656298611234213775836471231, A170741(27) = 524957740656298611234213775836471462. - 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 (20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, -210).

Cf. A170741 (G.f.: (1+x)/(1-21*x)).

coxG[{27,210,-20}] (* The coxG program is at A169452 *) (* Harvey P. Dale, Mar 02 2018 *)

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)/(210*t^27 - 20*t^26 - 20*t^25 - 20*t^24 - 20*t^23 - 20*t^22 - 20*t^21 - 20*t^20 - 20*t^19 - 20*t^18 - 20*t^17 - 20*t^16 - 20*t^15 - 20*t^14 - 20*t^13 - 20*t^12 - 20*t^11 - 20*t^10 - 20*t^9 - 20*t^8 - 20*t^7 - 20*t^6 - 20*t^5 - 20*t^4 - 20*t^3 - 20*t^2 - 20*t + 1).

A169227 Number of reduced words of length n in Coxeter group on 22 generators S_i with relations (S_i)^2 = (S_i S_j)^28 = I.

Original entry on oeis.org

1, 22, 462, 9702, 203742, 4278582, 89850222, 1886854662, 39623947902, 832102905942, 17474161024782, 366957381520422, 7706105011928862, 161828205250506102, 3398392310260628142, 71366238515473190982

Offset: 0

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

nonn

The initial terms coincide with those of A170741, although the two sequences are eventually different.
First disagreement at index 28: a(28) = 11024112553782270835918489292565900471, A170741(28) = 11024112553782270835918489292565900702. - 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 (20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, -210).

Cf. A170741 (G.f.: (1+x)/(1-21*x)).

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)/(210*t^28 - 20*t^27 - 20*t^26 - 20*t^25 - 20*t^24 - 20*t^23 - 20*t^22 - 20*t^21 - 20*t^20 - 20*t^19 - 20*t^18 - 20*t^17 - 20*t^16 - 20*t^15 - 20*t^14 - 20*t^13 - 20*t^12 - 20*t^11 - 20*t^10 - 20*t^9 - 20*t^8 - 20*t^7 - 20*t^6 - 20*t^5 - 20*t^4 - 20*t^3 - 20*t^2 - 20*t + 1).

A169275 Number of reduced words of length n in Coxeter group on 22 generators S_i with relations (S_i)^2 = (S_i S_j)^29 = I.

Original entry on oeis.org

1, 22, 462, 9702, 203742, 4278582, 89850222, 1886854662, 39623947902, 832102905942, 17474161024782, 366957381520422, 7706105011928862, 161828205250506102, 3398392310260628142, 71366238515473190982

Offset: 0

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

nonn

The initial terms coincide with those of A170741, although the two sequences are eventually different.
First disagreement at index 29: a(29) = 231506363629427687554288275143883914511, A170741(29) = 231506363629427687554288275143883914742. - 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 (20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, -210).

Cf. A170741 (G.f.: (1+x)/(1-21*x)).

coxG[{29,210,-20}] (* The coxG program is at A169452 *)  (* Harvey P. Dale, Sep 04 2023 *)

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)/(210*t^29 - 20*t^28 - 20*t^27 - 20*t^26 - 20*t^25 - 20*t^24 - 20*t^23 - 20*t^22 - 20*t^21 - 20*t^20 - 20*t^19 - 20*t^18 - 20*t^17 - 20*t^16 - 20*t^15 - 20*t^14 - 20*t^13 - 20*t^12 - 20*t^11 - 20*t^10 - 20*t^9 - 20*t^8 - 20*t^7 - 20*t^6 - 20*t^5 - 20*t^4 - 20*t^3 - 20*t^2 - 20*t + 1).

A169323 Number of reduced words of length n in Coxeter group on 22 generators S_i with relations (S_i)^2 = (S_i S_j)^30 = I.

Original entry on oeis.org

1, 22, 462, 9702, 203742, 4278582, 89850222, 1886854662, 39623947902, 832102905942, 17474161024782, 366957381520422, 7706105011928862, 161828205250506102, 3398392310260628142, 71366238515473190982

Offset: 0

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

nonn

The initial terms coincide with those of A170741, although the two sequences are eventually different.
First disagreement at index 30: a(30) = 4861633636217981438640053778021562209351, A170741(30) = 4861633636217981438640053778021562209582. - Klaus Brockhaus, Jun 22 2011
Computed with Magma using commands similar to those used to compute A154638.

Index entries for linear recurrences with constant coefficients, signature (20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, -210).

Cf. A170741 (G.f.: (1+x)/(1-21*x)).

coxG[{30,210,-20}] (* The coxG program is at A169452 *) (* Harvey P. Dale, Sep 23 2023 *)

G.f.: (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)/(210*t^30 - 20*t^29 - 20*t^28 - 20*t^27 - 20*t^26 - 20*t^25 - 20*t^24 - 20*t^23 - 20*t^22 - 20*t^21 - 20*t^20 - 20*t^19 - 20*t^18 - 20*t^17 - 20*t^16 - 20*t^15 - 20*t^14 - 20*t^13 - 20*t^12 - 20*t^11 - 20*t^10 - 20*t^9 - 20*t^8 - 20*t^7 - 20*t^6 - 20*t^5 - 20*t^4 - 20*t^3 - 20*t^2 - 20*t + 1).

cp's OEIS Frontend

A168891 Number of reduced words of length n in Coxeter group on 22 generators S_i with relations (S_i)^2 = (S_i S_j)^21 = I.

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A168939 Number of reduced words of length n in Coxeter group on 22 generators S_i with relations (S_i)^2 = (S_i S_j)^22 = I.

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A168987 Number of reduced words of length n in Coxeter group on 22 generators S_i with relations (S_i)^2 = (S_i S_j)^23 = I.

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A169035 Number of reduced words of length n in Coxeter group on 22 generators S_i with relations (S_i)^2 = (S_i S_j)^24 = I.

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A169083 Number of reduced words of length n in Coxeter group on 22 generators S_i with relations (S_i)^2 = (S_i S_j)^25 = I.

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A169131 Number of reduced words of length n in Coxeter group on 22 generators S_i with relations (S_i)^2 = (S_i S_j)^26 = I.

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A169179 Number of reduced words of length n in Coxeter group on 22 generators S_i with relations (S_i)^2 = (S_i S_j)^27 = I.

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A169227 Number of reduced words of length n in Coxeter group on 22 generators S_i with relations (S_i)^2 = (S_i S_j)^28 = I.

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A169275 Number of reduced words of length n in Coxeter group on 22 generators S_i with relations (S_i)^2 = (S_i S_j)^29 = I.

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