A170740 -id:A170740 - cp's OEIS frontend

A168842 Number of reduced words of length n in Coxeter group on 21 generators S_i with relations (S_i)^2 = (S_i S_j)^20 = I.

1, 21, 420, 8400, 168000, 3360000, 67200000, 1344000000, 26880000000, 537600000000, 10752000000000, 215040000000000, 4300800000000000, 86016000000000000, 1720320000000000000, 34406400000000000000

Offset: 0

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

nonn

The initial terms coincide with those of A170740, although the two sequences are eventually different.
First disagreement at index 20: a(20) = 110100479999999999999999790, A170740(20) = 110100480000000000000000000. - 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 (19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, -190).

Cf. A170740 (G.f.: (1+x)/(1-20*x)).

coxG[{20,190,-19}] (* The coxG program is at A169452 *) (* Harvey P. Dale, May 21 2017 *)

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)/(190*t^20 - 19*t^19 - 19*t^18 - 19*t^17 - 19*t^16 - 19*t^15 - 19*t^14 - 19*t^13 - 19*t^12 - 19*t^11 - 19*t^10 - 19*t^9 - 19*t^8 - 19*t^7 - 19*t^6 - 19*t^5 - 19*t^4 - 19*t^3 - 19*t^2 - 19*t + 1).

A168890 Number of reduced words of length n in Coxeter group on 21 generators S_i with relations (S_i)^2 = (S_i S_j)^21 = I.

Original entry on oeis.org

1, 21, 420, 8400, 168000, 3360000, 67200000, 1344000000, 26880000000, 537600000000, 10752000000000, 215040000000000, 4300800000000000, 86016000000000000, 1720320000000000000, 34406400000000000000

Offset: 0

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

nonn

The initial terms coincide with those of A170740, although the two sequences are eventually different.
First disagreement at index 21: a(21) = 2202009599999999999999999790, A170740(21) = 2202009600000000000000000000. - 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 (19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, -190).

Cf. A170740 (G.f.: (1+x)/(1-20*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)/(190*t^21 - 19*t^20 - 19*t^19 - 19*t^18 - 19*t^17 - 19*t^16 - 19*t^15 - 19*t^14 - 19*t^13 - 19*t^12 - 19*t^11 - 19*t^10 - 19*t^9 - 19*t^8 - 19*t^7 - 19*t^6 - 19*t^5 - 19*t^4 - 19*t^3 - 19*t^2 - 19*t + 1).

A168938 Number of reduced words of length n in Coxeter group on 21 generators S_i with relations (S_i)^2 = (S_i S_j)^22 = I.

Original entry on oeis.org

1, 21, 420, 8400, 168000, 3360000, 67200000, 1344000000, 26880000000, 537600000000, 10752000000000, 215040000000000, 4300800000000000, 86016000000000000, 1720320000000000000, 34406400000000000000

Offset: 0

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

nonn

The initial terms coincide with those of A170740, although the two sequences are eventually different.
First disagreement at index 22: a(22) = 44040191999999999999999999790, A170740(22) = 44040192000000000000000000000. - 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 (19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, -190).

Cf. A170740 (G.f.: (1+x)/(1-20*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)/(190*t^22 - 19*t^21 - 19*t^20 - 19*t^19 - 19*t^18 - 19*t^17 - 19*t^16 - 19*t^15 - 19*t^14 - 19*t^13 - 19*t^12 - 19*t^11 - 19*t^10 - 19*t^9 - 19*t^8 - 19*t^7 - 19*t^6 - 19*t^5 - 19*t^4 - 19*t^3 - 19*t^2 - 19*t + 1).

A168986 Number of reduced words of length n in Coxeter group on 21 generators S_i with relations (S_i)^2 = (S_i S_j)^23 = I.

Original entry on oeis.org

1, 21, 420, 8400, 168000, 3360000, 67200000, 1344000000, 26880000000, 537600000000, 10752000000000, 215040000000000, 4300800000000000, 86016000000000000, 1720320000000000000, 34406400000000000000

Offset: 0

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

nonn

The initial terms coincide with those of A170740, although the two sequences are eventually different.
First disagreement at index 23: a(23) = 880803839999999999999999999790, A170740(23) = 880803840000000000000000000000. - 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 (19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, -190).

Cf. A170740 (G.f.: (1+x)/(1-20*x)).

coxG[{23,190,-19}] (* The coxG program is at A169452 *) (* Harvey P. Dale, Nov 06 2017 *)

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)/(190*t^23 - 19*t^22 - 19*t^21 - 19*t^20 - 19*t^19 - 19*t^18 - 19*t^17 - 19*t^16 - 19*t^15 - 19*t^14 - 19*t^13 - 19*t^12 - 19*t^11 - 19*t^10 - 19*t^9 - 19*t^8 - 19*t^7 - 19*t^6 - 19*t^5 - 19*t^4 - 19*t^3 - 19*t^2 - 19*t + 1).

A169034 Number of reduced words of length n in Coxeter group on 21 generators S_i with relations (S_i)^2 = (S_i S_j)^24 = I.

Original entry on oeis.org

1, 21, 420, 8400, 168000, 3360000, 67200000, 1344000000, 26880000000, 537600000000, 10752000000000, 215040000000000, 4300800000000000, 86016000000000000, 1720320000000000000, 34406400000000000000

Offset: 0

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

nonn

The initial terms coincide with those of A170740, although the two sequences are eventually different.
First disagreement at index 24: a(24) = 17616076799999999999999999999790, A170740(24) = 17616076800000000000000000000000. - 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 (19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, -190).

Cf. A170740 (G.f.: (1+x)/(1-20*x)).

coxG[{24,190,-19}] (* The coxG program is at A169452 *) (* Harvey P. Dale, Oct 23 2015 *)

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)/(190*t^24 - 19*t^23 - 19*t^22 - 19*t^21 - 19*t^20 - 19*t^19 - 19*t^18 - 19*t^17 - 19*t^16 - 19*t^15 - 19*t^14 - 19*t^13 - 19*t^12 - 19*t^11 - 19*t^10 - 19*t^9 - 19*t^8 - 19*t^7 - 19*t^6 - 19*t^5 - 19*t^4 - 19*t^3 - 19*t^2 - 19*t + 1).

A169082 Number of reduced words of length n in Coxeter group on 21 generators S_i with relations (S_i)^2 = (S_i S_j)^25 = I.

Original entry on oeis.org

1, 21, 420, 8400, 168000, 3360000, 67200000, 1344000000, 26880000000, 537600000000, 10752000000000, 215040000000000, 4300800000000000, 86016000000000000, 1720320000000000000, 34406400000000000000

Offset: 0

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

nonn

The initial terms coincide with those of A170740, although the two sequences are eventually different.
First disagreement at index 25: a(25) = 352321535999999999999999999999790, A170740(25) = 352321536000000000000000000000000. - 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 (19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, -190).

Cf. A170740 (G.f.: (1+x)/(1-20*x)).

With[{num=Total[2t^Range[0,25]]-1-t^25,den=Total[-19 t^Range[24]] +190t^25+1},CoefficientList[Series[num/den,{t,0,40}],t]] (* Harvey P. Dale, Jun 14 2011 *)

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)/(190*t^25 - 19*t^24 - 19*t^23 - 19*t^22 - 19*t^21 - 19*t^20 - 19*t^19 - 19*t^18 - 19*t^17 - 19*t^16 - 19*t^15 - 19*t^14 - 19*t^13 - 19*t^12 - 19*t^11 - 19*t^10 - 19*t^9 - 19*t^8 - 19*t^7 - 19*t^6 - 19*t^5 - 19*t^4 - 19*t^3 - 19*t^2 - 19*t + 1).

A169130 Number of reduced words of length n in Coxeter group on 21 generators S_i with relations (S_i)^2 = (S_i S_j)^26 = I.

Original entry on oeis.org

1, 21, 420, 8400, 168000, 3360000, 67200000, 1344000000, 26880000000, 537600000000, 10752000000000, 215040000000000, 4300800000000000, 86016000000000000, 1720320000000000000, 34406400000000000000

Offset: 0

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

nonn

The initial terms coincide with those of A170740, although the two sequences are eventually different.
First disagreement at index 26: a(26) = 7046430719999999999999999999999790, A170740(26) = 7046430720000000000000000000000000. - 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 (19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, -190).

Cf. A170740 (G.f.: (1+x)/(1-20*x)).

coxG[{26,190,-19}] (* The coxG program is at A169452 *) (* Harvey P. Dale, Mar 24 2021 *)

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)/(190*t^26 - 19*t^25 - 19*t^24 - 19*t^23 - 19*t^22 - 19*t^21 - 19*t^20 - 19*t^19 - 19*t^18 - 19*t^17 - 19*t^16 - 19*t^15 - 19*t^14 - 19*t^13 - 19*t^12 - 19*t^11 - 19*t^10 - 19*t^9 - 19*t^8 - 19*t^7 - 19*t^6 - 19*t^5 - 19*t^4 - 19*t^3 - 19*t^2 - 19*t + 1).

A169178 Number of reduced words of length n in Coxeter group on 21 generators S_i with relations (S_i)^2 = (S_i S_j)^27 = I.

Original entry on oeis.org

1, 21, 420, 8400, 168000, 3360000, 67200000, 1344000000, 26880000000, 537600000000, 10752000000000, 215040000000000, 4300800000000000, 86016000000000000, 1720320000000000000, 34406400000000000000

Offset: 0

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

nonn

The initial terms coincide with those of A170740, although the two sequences are eventually different.
First disagreement at index 27: a(27) = 140928614399999999999999999999999790, A170740(27) = 140928614400000000000000000000000000. - 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 (19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, -190).

Cf. A170740 (G.f.: (1+x)/(1-20*x)).

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)/(190*t^27 - 19*t^26 - 19*t^25 - 19*t^24 - 19*t^23 - 19*t^22 - 19*t^21 - 19*t^20 - 19*t^19 - 19*t^18 - 19*t^17 - 19*t^16 - 19*t^15 - 19*t^14 - 19*t^13 - 19*t^12 - 19*t^11 - 19*t^10 - 19*t^9 - 19*t^8 - 19*t^7 - 19*t^6 - 19*t^5 - 19*t^4 - 19*t^3 - 19*t^2 - 19*t + 1).

A169226 Number of reduced words of length n in Coxeter group on 21 generators S_i with relations (S_i)^2 = (S_i S_j)^28 = I.

Original entry on oeis.org

1, 21, 420, 8400, 168000, 3360000, 67200000, 1344000000, 26880000000, 537600000000, 10752000000000, 215040000000000, 4300800000000000, 86016000000000000, 1720320000000000000, 34406400000000000000

Offset: 0

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

nonn

The initial terms coincide with those of A170740, although the two sequences are eventually different.
First disagreement at index 28: a(28) = 2818572287999999999999999999999999790, A170740(28) = 2818572288000000000000000000000000000. - 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 (19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, -190).

Cf. A170740 (G.f.: (1+x)/(1-20*x)).

With[{num=Total[2t^Range[27]]+t^28+1,den=Total[-19 t^Range[27]]+190t^28+ 1},CoefficientList[Series[num/den ,{t,0,20}],t]] (* Harvey P. Dale, Dec 24 2013 *)

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)/(190*t^28 - 19*t^27 - 19*t^26 - 19*t^25 - 19*t^24 - 19*t^23 - 19*t^22 - 19*t^21 - 19*t^20 - 19*t^19 - 19*t^18 - 19*t^17 - 19*t^16 - 19*t^15 - 19*t^14 - 19*t^13 - 19*t^12 - 19*t^11 - 19*t^10 - 19*t^9 - 19*t^8 - 19*t^7 - 19*t^6 - 19*t^5 - 19*t^4 - 19*t^3 - 19*t^2 - 19*t + 1).

A169274 Number of reduced words of length n in Coxeter group on 21 generators S_i with relations (S_i)^2 = (S_i S_j)^29 = I.

Original entry on oeis.org

1, 21, 420, 8400, 168000, 3360000, 67200000, 1344000000, 26880000000, 537600000000, 10752000000000, 215040000000000, 4300800000000000, 86016000000000000, 1720320000000000000, 34406400000000000000

Offset: 0

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

nonn

The initial terms coincide with those of A170740, although the two sequences are eventually different.
First disagreement at index 29: a(29) = 56371445759999999999999999999999999790, A170740(29) = 56371445760000000000000000000000000000. - 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 (19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, 19, -190).

Cf. A170740 (G.f.: (1+x)/(1-20*x)).

With[{num=Total[2t^Range[28]]+t^29+1,den=Total[-19 t^Range[28]]+ 190t^29+ 1}, CoefficientList[Series[num/den,{t,0,20}],t]] (* Harvey P. Dale, Jul 19 2012 *)

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)/(190*t^29 - 19*t^28 - 19*t^27 - 19*t^26 - 19*t^25 - 19*t^24 - 19*t^23 - 19*t^22 - 19*t^21 - 19*t^20 - 19*t^19 - 19*t^18 - 19*t^17 - 19*t^16 - 19*t^15 - 19*t^14 - 19*t^13 - 19*t^12 - 19*t^11 - 19*t^10 - 19*t^9 - 19*t^8 - 19*t^7 - 19*t^6 - 19*t^5 - 19*t^4 - 19*t^3 - 19*t^2 - 19*t + 1).

cp's OEIS Frontend

A168842 Number of reduced words of length n in Coxeter group on 21 generators S_i with relations (S_i)^2 = (S_i S_j)^20 = I.

Views

Author

Keywords

Comments

Links

Crossrefs

Programs

Mathematica

Formula

A168890 Number of reduced words of length n in Coxeter group on 21 generators S_i with relations (S_i)^2 = (S_i S_j)^21 = I.

Views

Author

Keywords

Comments

Links

Crossrefs

Formula

A168938 Number of reduced words of length n in Coxeter group on 21 generators S_i with relations (S_i)^2 = (S_i S_j)^22 = I.

Views

Author

Keywords

Comments

Links

Crossrefs

Formula

A168986 Number of reduced words of length n in Coxeter group on 21 generators S_i with relations (S_i)^2 = (S_i S_j)^23 = I.

Views

Author

Keywords

Comments

Links

Crossrefs

Programs

Mathematica

Formula

A169034 Number of reduced words of length n in Coxeter group on 21 generators S_i with relations (S_i)^2 = (S_i S_j)^24 = I.

Views

Author

Keywords

Comments

Links

Crossrefs

Programs

Mathematica

Formula

A169082 Number of reduced words of length n in Coxeter group on 21 generators S_i with relations (S_i)^2 = (S_i S_j)^25 = I.

Views

Author

Keywords

Comments

Links

Crossrefs

Programs

Mathematica

Formula

A169130 Number of reduced words of length n in Coxeter group on 21 generators S_i with relations (S_i)^2 = (S_i S_j)^26 = I.

Views

Author

Keywords

Comments

Links

Crossrefs

Programs

Mathematica

Formula

A169178 Number of reduced words of length n in Coxeter group on 21 generators S_i with relations (S_i)^2 = (S_i S_j)^27 = I.

Views

Author

Keywords

Comments

Links

Crossrefs

Formula

A169226 Number of reduced words of length n in Coxeter group on 21 generators S_i with relations (S_i)^2 = (S_i S_j)^28 = I.

Views

Author

Keywords

Comments