A170744 -id:A170744 - cp's OEIS frontend

A168846 Number of reduced words of length n in Coxeter group on 25 generators S_i with relations (S_i)^2 = (S_i S_j)^20 = I.

1, 25, 600, 14400, 345600, 8294400, 199065600, 4777574400, 114661785600, 2751882854400, 66045188505600, 1585084524134400, 38042028579225600, 913008685901414400, 21912208461633945600, 525893003079214694400

Offset: 0

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

nonn

The initial terms coincide with those of A170744, although the two sequences are eventually different.
First disagreement at index 20: a(20) = 4187488247750628826782105300, A170744(20) = 4187488247750628826782105600. - Klaus Brockhaus, Apr 02 2011
Computed with MAGMA using commands similar to those used to compute A154638.

Index entries for linear recurrences with constant coefficients, signature (23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, -276).

Cf. A170744 (G.f.: (1+x)/(1-24*x)).

With[{num=Total[2t^Range[19]]+t^20+1,den=Total[-23 t^Range[19]]+ 276t^20+ 1}, CoefficientList[Series[num/den,{t,0,20}],t]] (* Harvey P. Dale, Jul 20 2011 *)

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)/(276*t^20 - 23*t^19 - 23*t^18 - 23*t^17 - 23*t^16 - 23*t^15 - 23*t^14 - 23*t^13 - 23*t^12 - 23*t^11 - 23*t^10 - 23*t^9 - 23*t^8 - 23*t^7 - 23*t^6 - 23*t^5 - 23*t^4 - 23*t^3 - 23*t^2 - 23*t + 1).

A168894 Number of reduced words of length n in Coxeter group on 25 generators S_i with relations (S_i)^2 = (S_i S_j)^21 = I.

Original entry on oeis.org

1, 25, 600, 14400, 345600, 8294400, 199065600, 4777574400, 114661785600, 2751882854400, 66045188505600, 1585084524134400, 38042028579225600, 913008685901414400, 21912208461633945600, 525893003079214694400

Offset: 0

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

nonn

The initial terms coincide with those of A170744, although the two sequences are eventually different.
First disagreement at index 21: a(21) = 100499717946015091842770534100, A170744(21) = 100499717946015091842770534400. - 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 (23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, -276).

Cf. A170744 (G.f.: (1+x)/(1-24*x)).

coxG[{21,276,-23}] (* The coxG program is at A169452 *) (* Harvey P. Dale, Sep 19 2020 *)

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)/(276*t^21 - 23*t^20 - 23*t^19 - 23*t^18 - 23*t^17 - 23*t^16 - 23*t^15 - 23*t^14 - 23*t^13 - 23*t^12 - 23*t^11 - 23*t^10 - 23*t^9 - 23*t^8 - 23*t^7 - 23*t^6 - 23*t^5 - 23*t^4 - 23*t^3 - 23*t^2 - 23*t + 1).

A168942 Number of reduced words of length n in Coxeter group on 25 generators S_i with relations (S_i)^2 = (S_i S_j)^22 = I.

Original entry on oeis.org

1, 25, 600, 14400, 345600, 8294400, 199065600, 4777574400, 114661785600, 2751882854400, 66045188505600, 1585084524134400, 38042028579225600, 913008685901414400, 21912208461633945600, 525893003079214694400

Offset: 0

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

nonn

The initial terms coincide with those of A170744, although the two sequences are eventually different.
First disagreement at index 22: a(22) = 2411993230704362204226492825300, A170744(22) = 2411993230704362204226492825600. - Klaus Brockhaus, Apr 10 2011
Computed with MAGMA using commands similar to those used to compute A154638.

Index entries for linear recurrences with constant coefficients, signature (23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, -276).

Cf. A170744 (G.f.: (1+x)/(1-24*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)/(276*t^22 - 23*t^21 - 23*t^20 - 23*t^19 - 23*t^18 - 23*t^17 - 23*t^16 - 23*t^15 - 23*t^14 - 23*t^13 - 23*t^12 - 23*t^11 - 23*t^10 - 23*t^9 - 23*t^8 - 23*t^7 - 23*t^6 - 23*t^5 - 23*t^4 - 23*t^3 - 23*t^2 - 23*t + 1).

A168990 Number of reduced words of length n in Coxeter group on 25 generators S_i with relations (S_i)^2 = (S_i S_j)^23 = I.

Original entry on oeis.org

1, 25, 600, 14400, 345600, 8294400, 199065600, 4777574400, 114661785600, 2751882854400, 66045188505600, 1585084524134400, 38042028579225600, 913008685901414400, 21912208461633945600, 525893003079214694400

Offset: 0

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

nonn

The initial terms coincide with those of A170744, although the two sequences are eventually different.
First disagreement at index 23: a(23) = 57887837536904692901435827814100, A170744(23) = 57887837536904692901435827814400. - 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 (23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, -276).

Cf. A170744 (G.f.: (1+x)/(1-24*x)).

coxG[{23,276,-23}] (* The coxG program is at A169452 *) (* Harvey P. Dale, Apr 30 2022 *)

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)/(276*t^23 - 23*t^22 - 23*t^21 - 23*t^20 - 23*t^19 - 23*t^18 - 23*t^17 - 23*t^16 - 23*t^15 - 23*t^14 - 23*t^13 - 23*t^12 - 23*t^11 - 23*t^10 - 23*t^9 - 23*t^8 - 23*t^7 - 23*t^6 - 23*t^5 - 23*t^4 - 23*t^3 - 23*t^2 - 23*t + 1).

A169038 Number of reduced words of length n in Coxeter group on 25 generators S_i with relations (S_i)^2 = (S_i S_j)^24 = I.

Original entry on oeis.org

1, 25, 600, 14400, 345600, 8294400, 199065600, 4777574400, 114661785600, 2751882854400, 66045188505600, 1585084524134400, 38042028579225600, 913008685901414400, 21912208461633945600, 525893003079214694400

Offset: 0

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

nonn

The initial terms coincide with those of A170744, although the two sequences are eventually different.
First disagreement at index 24: a(24) = 1389308100885712629634459867545300, A170744(24) = 1389308100885712629634459867545600. - 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 (23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, -276).

Cf. A170744 (G.f.: (1+x)/(1-24*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)/(276*t^24 - 23*t^23 - 23*t^22 - 23*t^21 - 23*t^20 - 23*t^19 - 23*t^18 - 23*t^17 - 23*t^16 - 23*t^15 - 23*t^14 - 23*t^13 - 23*t^12 - 23*t^11 - 23*t^10 - 23*t^9 - 23*t^8 - 23*t^7 - 23*t^6 - 23*t^5 - 23*t^4 - 23*t^3 - 23*t^2 - 23*t + 1).

A169086 Number of reduced words of length n in Coxeter group on 25 generators S_i with relations (S_i)^2 = (S_i S_j)^25 = I.

Original entry on oeis.org

1, 25, 600, 14400, 345600, 8294400, 199065600, 4777574400, 114661785600, 2751882854400, 66045188505600, 1585084524134400, 38042028579225600, 913008685901414400, 21912208461633945600, 525893003079214694400

Offset: 0

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

nonn

The initial terms coincide with those of A170744, although the two sequences are eventually different.
First disagreement at index 25: a(25) = 33343394421257103111227036821094100, A170744(25) = 33343394421257103111227036821094400. - 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 (23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, -276).

Cf. A170744 (G.f.: (1+x)/(1-24*x)).

coxG[{25,276,-23}] (* The coxG program is at A169452 *) (* Harvey P. Dale, Jun 19 2018 *)

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)/(276*t^25 - 23*t^24 - 23*t^23 - 23*t^22 - 23*t^21 - 23*t^20 - 23*t^19 - 23*t^18 - 23*t^17 - 23*t^16 - 23*t^15 - 23*t^14 - 23*t^13 - 23*t^12 - 23*t^11 - 23*t^10 - 23*t^9 - 23*t^8 - 23*t^7 - 23*t^6 - 23*t^5 - 23*t^4 - 23*t^3 - 23*t^2 - 23*t + 1).

A169134 Number of reduced words of length n in Coxeter group on 25 generators S_i with relations (S_i)^2 = (S_i S_j)^26 = I.

Original entry on oeis.org

1, 25, 600, 14400, 345600, 8294400, 199065600, 4777574400, 114661785600, 2751882854400, 66045188505600, 1585084524134400, 38042028579225600, 913008685901414400, 21912208461633945600, 525893003079214694400

Offset: 0

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

nonn

The initial terms coincide with those of A170744, although the two sequences are eventually different.
First disagreement at index 26: a(26) = 800241466110170474669448883706265300, A170744(26) = 800241466110170474669448883706265600. - 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 (23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, -276).

Cf. A170744 (G.f.: (1+x)/(1-24*x)).

coxG[{26,276,-23}] (* The coxG program is at A169452 *) (* Harvey P. Dale, Aug 25 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)/(276*t^26 - 23*t^25 - 23*t^24 - 23*t^23 - 23*t^22 - 23*t^21 - 23*t^20 - 23*t^19 - 23*t^18 - 23*t^17 - 23*t^16 - 23*t^15 - 23*t^14 - 23*t^13 - 23*t^12 - 23*t^11 - 23*t^10 - 23*t^9 - 23*t^8 - 23*t^7 - 23*t^6 - 23*t^5 - 23*t^4 - 23*t^3 - 23*t^2 - 23*t + 1).

A169182 Number of reduced words of length n in Coxeter group on 25 generators S_i with relations (S_i)^2 = (S_i S_j)^27 = I.

Original entry on oeis.org

1, 25, 600, 14400, 345600, 8294400, 199065600, 4777574400, 114661785600, 2751882854400, 66045188505600, 1585084524134400, 38042028579225600, 913008685901414400, 21912208461633945600, 525893003079214694400

Offset: 0

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

nonn

The initial terms coincide with those of A170744, although the two sequences are eventually different.
First disagreement at index 27: a(27) = 19205795186644091392066773208950374100, A170744(27) = 19205795186644091392066773208950374400. - 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 (23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, -276).

Cf. A170744 (G.f.: (1+x)/(1-24*x)).

coxG[{27,276,-23}] (* The coxG program is at A169452 *) (* Harvey P. Dale, Jan 20 2015 *)

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)/(276*t^27 - 23*t^26 - 23*t^25 - 23*t^24 - 23*t^23 - 23*t^22 - 23*t^21 - 23*t^20 - 23*t^19 - 23*t^18 - 23*t^17 - 23*t^16 - 23*t^15 - 23*t^14 - 23*t^13 - 23*t^12 - 23*t^11 - 23*t^10 - 23*t^9 - 23*t^8 - 23*t^7 - 23*t^6 - 23*t^5 - 23*t^4 - 23*t^3 - 23*t^2 - 23*t + 1).

A169230 Number of reduced words of length n in Coxeter group on 25 generators S_i with relations (S_i)^2 = (S_i S_j)^28 = I.

Original entry on oeis.org

1, 25, 600, 14400, 345600, 8294400, 199065600, 4777574400, 114661785600, 2751882854400, 66045188505600, 1585084524134400, 38042028579225600, 913008685901414400, 21912208461633945600, 525893003079214694400

Offset: 0

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

nonn

The initial terms coincide with those of A170744, although the two sequences are eventually different.
First disagreement at index 28: a(28) = 460939084479458193409602557014808985300, A170744(28) = 460939084479458193409602557014808985600. - 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 (23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, -276).

Cf. A170744 (G.f.: (1+x)/(1-24*x)).

With[{num=Total[2t^Range[27]]+t^28+1,den=Total[-23 t^Range[27]]+ 276t^28+ 1}, CoefficientList[Series[num/den,{t,0,20}],t]] (* Harvey P. Dale, Nov 04 2011 *)

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)/(276*t^28 - 23*t^27 - 23*t^26 - 23*t^25 - 23*t^24 - 23*t^23 - 23*t^22 - 23*t^21 - 23*t^20 - 23*t^19 - 23*t^18 - 23*t^17 - 23*t^16 - 23*t^15 - 23*t^14 - 23*t^13 - 23*t^12 - 23*t^11 - 23*t^10 - 23*t^9 - 23*t^8 - 23*t^7 - 23*t^6 - 23*t^5 - 23*t^4 - 23*t^3 - 23*t^2 - 23*t + 1).

A169278 Number of reduced words of length n in Coxeter group on 25 generators S_i with relations (S_i)^2 = (S_i S_j)^29 = I.

Original entry on oeis.org

1, 25, 600, 14400, 345600, 8294400, 199065600, 4777574400, 114661785600, 2751882854400, 66045188505600, 1585084524134400, 38042028579225600, 913008685901414400, 21912208461633945600, 525893003079214694400

Offset: 0

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

nonn

The initial terms coincide with those of A170744, although the two sequences are eventually different.
First disagreement at index 29: a(29) = 11062538027506996641830461368355415654100, A170744(29) = 11062538027506996641830461368355415654400. - 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 (23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, -276).

Cf. A170744 (G.f.: (1+x)/(1-24*x)).

coxG[{29,276,-23}] (* The coxG program is at A169452 *) (* Harvey P. Dale, Mar 21 2025 *)

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)/(276*t^29 - 23*t^28 - 23*t^27 - 23*t^26 - 23*t^25 - 23*t^24 - 23*t^23 - 23*t^22 - 23*t^21 - 23*t^20 - 23*t^19 - 23*t^18 - 23*t^17 - 23*t^16 - 23*t^15 - 23*t^14 - 23*t^13 - 23*t^12 - 23*t^11 - 23*t^10 - 23*t^9 - 23*t^8 - 23*t^7 - 23*t^6 - 23*t^5 - 23*t^4 - 23*t^3 - 23*t^2 - 23*t + 1).

cp's OEIS Frontend

A168846 Number of reduced words of length n in Coxeter group on 25 generators S_i with relations (S_i)^2 = (S_i S_j)^20 = I.

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A168894 Number of reduced words of length n in Coxeter group on 25 generators S_i with relations (S_i)^2 = (S_i S_j)^21 = I.

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A168942 Number of reduced words of length n in Coxeter group on 25 generators S_i with relations (S_i)^2 = (S_i S_j)^22 = I.

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A168990 Number of reduced words of length n in Coxeter group on 25 generators S_i with relations (S_i)^2 = (S_i S_j)^23 = I.

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A169038 Number of reduced words of length n in Coxeter group on 25 generators S_i with relations (S_i)^2 = (S_i S_j)^24 = I.

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A169086 Number of reduced words of length n in Coxeter group on 25 generators S_i with relations (S_i)^2 = (S_i S_j)^25 = I.

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A169134 Number of reduced words of length n in Coxeter group on 25 generators S_i with relations (S_i)^2 = (S_i S_j)^26 = I.

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A169182 Number of reduced words of length n in Coxeter group on 25 generators S_i with relations (S_i)^2 = (S_i S_j)^27 = I.

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A169230 Number of reduced words of length n in Coxeter group on 25 generators S_i with relations (S_i)^2 = (S_i S_j)^28 = I.

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