A154638 -id:A154638 - cp's OEIS frontend

A166608 Number of reduced words of length n in Coxeter group on 22 generators S_i with relations (S_i)^2 = (S_i S_j)^12 = I.

1, 22, 462, 9702, 203742, 4278582, 89850222, 1886854662, 39623947902, 832102905942, 17474161024782, 366957381520422, 7706105011928631, 161828205250496400, 3398392310260322760, 71366238515464643520

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.

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 (20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, -210).

R:=PowerSeriesRing(Integers(), 20); Coefficients(R!( (1+x)*(1-x^12)/(1 -21*x +230*x^12 -210*x^13) )); // G. C. Greubel, Apr 25 2019

CoefficientList[Series[(1+x)*(1-x^12)/(1 -21*x +230*x^12 -210*x^13), {x, 0, 20}], x] (* G. C. Greubel, May 18 2016, modified Apr 25 2019 *)
coxG[{12,210,-20}] (* The coxG program is at A169452 *) (* Harvey P. Dale, Jul 20 2018 *)

my(x='x+O('x^20)); Vec((1+x)*(1-x^12)/(1 -21*x +230*x^12 -210*x^13)) \\ G. C. Greubel, Apr 25 2019

((1+x)*(1-x^12)/(1 -21*x +230*x^12 -210*x^13)).series(x, 20).coefficients(x, sparse=False) # G. C. Greubel, Apr 25 2019

G.f.: (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^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).

G.f.: (1+x)*(1-x^12)/(1 -21*x +230*x^12 -210*x^13). - G. C. Greubel, Apr 25 2019

A166610 Number of reduced words of length n in Coxeter group on 23 generators S_i with relations (S_i)^2 = (S_i S_j)^12 = I.

Original entry on oeis.org

1, 23, 506, 11132, 244904, 5387888, 118533536, 2607737792, 57370231424, 1262145091328, 27767192009216, 610878224202752, 13439320932460291, 295665060514120836, 6504631331310536193, 143101889288829107868

Offset: 0

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

nonn

The initial terms coincide with those of A170742, although the two sequences are eventually different.

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 (21, 21, 21, 21, 21, 21, 21, 21, 21, 21, 21, -231).

R:=PowerSeriesRing(Integers(), 20); Coefficients(R!( (1+x)*(1-x^12)/(1-22*x+252*x^12-231*x^13) )); // G. C. Greubel, Apr 25 2019

coxG[{12,231,-21}] (* The coxG program is at A169452 *) (* Harvey P. Dale, Feb 03 2015 *)
CoefficientList[Series[(1+x)*(1-x^12)/(1-22*x+252*x^12-231*x^13), {x, 0, 20}], x] (* G. C. Greubel, May 18 2016, modified Apr 25 2019 *)

my(x='x+O('x^20)); Vec((1+x)*(1-x^12)/(1-22*x+252*x^12-231*x^13)) \\ G. C. Greubel, Apr 25 2019

((1+x)*(1-x^12)/(1-22*x+252*x^12-231*x^13)).series(x, 20).coefficients(x, sparse=False) # G. C. Greubel, Apr 25 2019

G.f.: (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)/(231*t^12 - 21*t^11 - 21*t^10 - 21*t^9 -21*t^8 -21*t^7 - 21*t^6 - 21*t^5 - 21*t^4 - 21*t^3 - 21*t^2 -21*t + 1).

G.f.: (1+x)*(1-x^12)/(1 -22*x + 252*x^12 - 231*x^13). - G. C. Greubel, Apr 25 2019

A167882 Number of reduced words of length n in Coxeter group on 4 generators S_i with relations (S_i)^2 = (S_i S_j)^16 = I.

Original entry on oeis.org

1, 4, 12, 36, 108, 324, 972, 2916, 8748, 26244, 78732, 236196, 708588, 2125764, 6377292, 19131876, 57395622, 172186848, 516560496, 1549681344, 4649043600, 13947129504, 41841384624, 125524142208, 376572391632, 1129717069920

Offset: 0

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

nonn

The initial terms coincide with those of A003946, although the two sequences are eventually different.

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 (2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,-3).

Cf. A003946, A154638, A169452.

R:=PowerSeriesRing(Integers(), 40); Coefficients(R!( (1+x)*(1-x^16)/(1-3*x+5*x^16-3*x^17) )); // G. C. Greubel, Dec 06 2024

CoefficientList[Series[(1+t)*(1-t^16)/(1-3*t+5*t^16-3*t^17), {t,0,50}], t] (* G. C. Greubel, Jun 29 2016; Dec 06 2024 *)
coxG[{16,3,-2}] (* The coxG program is at A169452 *) (* G. C. Greubel, Dec 06 2024 *)

def A167882_list(prec):
    P. = PowerSeriesRing(ZZ, prec)
    return P( (1+x)*(1-x^16)/(1-3*x+5*x^16-3*x^17) ).list()
print(A167882_list(40)) # G. C. Greubel, Dec 06 2024

G.f.: (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) / ( 3*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).
From G. C. Greubel, Jan 17 2023: (Start)
a(n) = 2*Sum_{j=1..15} a(n-j) - 3*a(n-16).
G.f.: (1+x)*(1-x^16)/(1 - 3*x + 5*x^16 - 3*x^17). (End)

A167896 Number of reduced words of length n in Coxeter group on 5 generators S_i with relations (S_i)^2 = (S_i S_j)^16 = I.

Original entry on oeis.org

1, 5, 20, 80, 320, 1280, 5120, 20480, 81920, 327680, 1310720, 5242880, 20971520, 83886080, 335544320, 1342177280, 5368709110, 21474836400, 85899345450, 343597381200, 1374389522400, 5497558080000, 21990232281600, 87960928972800

Offset: 0

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

nonn

The initial terms coincide with those of A003947, although the two sequences are eventually different.

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 (3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,-6).

Cf. A003947, A154639, A169452.

R:=PowerSeriesRing(Integers(), 40); Coefficients(R!( (1+x)*(1-x^16)/(1-4*x+9*x^16-6*x^17) )); // G. C. Greubel, Dec 06 2024

CoefficientList[Series[(1+t)*(1-t^16)/(1-4*t+9*t^16-6*t^17), {t,0,50}], t] (* G. C. Greubel, Jul 01 2016; Dec 06 2024 *)
coxG[{16,6,-3,40}] (* The coxG program is at A169452 *) (* G. C. Greubel, Dec 06 2024 *)

def A167896_list(prec):
    P. = PowerSeriesRing(ZZ, prec)
    return P( (1+x)*(1-x^16)/(1-4*x+9*x^16-6*x^17) ).list()
print(A167896_list(40)) # G. C. Greubel, Dec 06 2024

G.f.: (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)/ ( 6*t^16 - 3*t^15 - 3*t^14 - 3*t^13 - 3*t^12 - 3*t^11 - 3*t^10 - 3*t^9 - 3*t^8 - 3*t^7 - 3*t^6 - 3*t^5 - 3*t^4 - 3*t^3 - 3*t^2 - 3*t + 1).
From G. C. Greubel, Dec 06 2024: (Start)
a(n) = 3*Sum_{j=1..15} a(n-j) - 6*a(n-16).
G.f.: (1+x)*(1-x^16)/(1 - 4*x + 9*x^16 - 6*x^17). (End)

A167900 Number of reduced words of length n in Coxeter group on 9 generators S_i with relations (S_i)^2 = (S_i S_j)^16 = I.

Original entry on oeis.org

1, 9, 72, 576, 4608, 36864, 294912, 2359296, 18874368, 150994944, 1207959552, 9663676416, 77309411328, 618475290624, 4947802324992, 39582418599936, 316659348799452, 2533274790395328, 20266198323160356, 162129586585264704

Offset: 0

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

nonn

The initial terms coincide with those of A003951, although the two sequences are eventually different.

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 (7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,-28).

Cf. A003951, A154638, A169452.

R:=PowerSeriesRing(Integers(), 40); Coefficients(R!( (1+x)*(1-x^16)/(1-8*x+35*x^16-28*x^17) )); // G. C. Greubel, Dec 06 2024

CoefficientList[Series[(1+t)*(1-t^16)/(1-8*t+35*t^16-28*t^17), {t,0,50}], t] (* G. C. Greubel, Jul 01 2016; Dec 06 2024 *)
coxG[{16,28,-7}] (* The coxG program is at A169452 *) (* G. C. Greubel, Dec 06 2024 *)

def A167900_list(prec):
    P. = PowerSeriesRing(ZZ, prec)
    return P( (1+x)*(1-x^16)/(1-8*x+35*x^16-28*x^17) ).list()
print(A167900_list(40)) # G. C. Greubel, Dec 06 2024

G.f.: (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)/( 28*t^16 - 7*t^15 - 7*t^14 - 7*t^13 - 7*t^12 - 7*t^11 - 7*t^10 - 7*t^9 - 7*t^8 - 7*t^7 - 7*t^6 - 7*t^5 - 7*t^4 - 7*t^3 - 7*t^2 - 7*t + 1).
From G. C. Greubel, Dec 06 2024: (Start)
a(n) = 7*Sum_{j=1..15} a(n-j) - 28*a(n-16).
G.f.: (1+x)*(1-x^16)/(1 - 8*x + 35*x^16 - 28*x^17). (End)

A167908 Number of reduced words of length n in Coxeter group on 10 generators S_i with relations (S_i)^2 = (S_i S_j)^16 = I.

Original entry on oeis.org

1, 10, 90, 810, 7290, 65610, 590490, 5314410, 47829690, 430467210, 3874204890, 34867844010, 313810596090, 2824295364810, 25418658283290, 228767924549610, 2058911320946445, 18530201888517600, 166771816996654800

Offset: 0

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

nonn

The initial terms coincide with those of A003952, although the two sequences are eventually different.

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 (8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,-36).

Cf. A003952, A154638, A169452.

R:=PowerSeriesRing(Integers(), 30);
Coefficients(R!( (1+x)*(1-x^16)/(1-9*x+44*x^16-36*x^17) )); // G. C. Greubel, Jul 23 2024

With[{a=36, b=8}, CoefficientList[Series[(1+t)*(1-t^16)/(1-(b+1)*t +(a + b)*t^16 -a*t^17), {t,0,40}], t]] (* G. C. Greubel, Jul 01 2016; Jul 23 2024 *)
coxG[{16,36,-8}] (* The coxG program is at A169452 *) (* Harvey P. Dale, Jun 04 2017 *)

def A167908_list(prec):
    P. = PowerSeriesRing(ZZ, prec)
    return P( (1+x)*(1-x^16)/(1-9*x+44*x^16-36*x^17) ).list()
A167908_list(30) # G. C. Greubel, Jul 23 2024

G.f.: (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)/( 36*t^16 - 8*t^15 - 8*t^14 - 8*t^13 - 8*t^12 - 8*t^11 - 8*t^10 - 8*t^9 - 8*t^8 - 8*t^7 - 8*t^6 - 8*t^5 - 8*t^4 - 8*t^3 - 8*t^2 - 8*t + 1).
From G. C. Greubel, Jul 23 2024: (Start)
a(n) = 8*Sum_{j=1..15} a(n-j) - 36*a(n-16).
G.f.: (1+t)*(1 - t^16)/(1 - 9*t + 44*t^16 - 36*t^17). (End)

A167914 Number of reduced words of length n in Coxeter group on 11 generators S_i with relations (S_i)^2 = (S_i S_j)^16 = I.

Original entry on oeis.org

1, 11, 110, 1100, 11000, 110000, 1100000, 11000000, 110000000, 1100000000, 11000000000, 110000000000, 1100000000000, 11000000000000, 110000000000000, 1100000000000000, 10999999999999945, 109999999999998900

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.

G. C. Greubel, Table of n, a(n) for n = 0..500
Index entries for linear recurrences with constant coefficients, signature (9,9,9,9,9,9,9,9,9,9,9,9,9,9,9,-45).

Cf. A003953, A154638, A169452.

R:=PowerSeriesRing(Integers(), 40);
Coefficients(R!( (1+x)*(1-x^16)/(1-10*x+54*x^16-45*x^17) )); // G. C. Greubel, Dec 04 2024

CoefficientList[Series[(1+t)*(1-t^16)/(1-10*t+54*t^16-45*t^17), {t,0,50}], t] (* G. C. Greubel, Jul 01 2016; Dec 04 2024 *)
coxG[{16,45,-9}] (* The coxG program is at A169452 *) (* G. C. Greubel, Dec 04 2024 *)

def A167914_list(prec):
    P. = PowerSeriesRing(ZZ, prec)
    return P( (1+x)*(1-x^16)/(1-10*x+54*x^16-45*x^17) ).list()
A167914_list(40) # G. C. Greubel, Dec 04 2024

G.f.: (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^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).
From G. C. Greubel, Dec 04 2024: (Start)
a(n) = 9*Sum_{j=1..15} a(n-j) - 45*a(n-16).
G.f.: (1+x)*(1-x^16)/(1 - 10*x + 54*x^16 - 45*x^17). (End)

A167916 Number of reduced words of length n in Coxeter group on 12 generators S_i with relations (S_i)^2 = (S_i S_j)^16 = I.

Original entry on oeis.org

1, 12, 132, 1452, 15972, 175692, 1932612, 21258732, 233846052, 2572306572, 28295372292, 311249095212, 3423740047332, 37661140520652, 414272545727172, 4556998002998892, 50126978032987746, 551396758362864480

Offset: 0

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

nonn

The initial terms coincide with those of A003954, although the two sequences are eventually different.

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 (10,10,10,10,10,10,10,10,10,10,10,10,10,10,10,-55).

Cf. A003954, A154638, A169452.

R:=PowerSeriesRing(Integers(), 30); Coefficients(R!( (1+x)*(1-x^16)/(1-11*x+65*x^16-55*x^17) )); // G. C. Greubel, Nov 10 2023

CoefficientList[Series[(1+t)*(1-t^16)/(1-11*t+65*t^16-55*t^17), {t,0,50}], t] (* G. C. Greubel, Jul 01 2016; Nov 10 2023 *)
coxG[{16,55,-10}] (* The coxG program is at A169452 *) (* G. C. Greubel, Nov 10 2023 *)

def A167916_list(prec):
    P. = PowerSeriesRing(ZZ, prec)
    return P( (1+x)*(1-x^16)/(1-11*x+65*x^16-55*x^17) ).list()
A167916_list(30) # G. C. Greubel, Nov 10 2023

G.f.: (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)/( 55*t^16 - 10*t^15 - 10*t^14 - 10*t^13 - 10*t^12 - 10*t^11 - 10*t^10 - 10*t^9 - 10*t^8 - 10*t^7 - 10*t^6 - 10*t^5 - 10*t^4 - 10*t^3 - 10*t^2 - 10*t + 1).
From G. C. Greubel, Nov 10 2023: (Start)
a(n) = 10*Sum_{j=1..15} a(n-j) - 55*a(n-16).
G.f.: (1+x)*(1-x^16)/(1 - 11*x + 65*x^16 - 55*x^17). (End)

A167923 Number of reduced words of length n in Coxeter group on 15 generators S_i with relations (S_i)^2 = (S_i S_j)^16 = I.

Original entry on oeis.org

1, 15, 210, 2940, 41160, 576240, 8067360, 112943040, 1581202560, 22136835840, 309915701760, 4338819824640, 60743477544960, 850408685629440, 11905721598812160, 166680102383370240, 2333521433367183255

Offset: 0

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

nonn

The initial terms coincide with those of A170734, although the two sequences are eventually different.

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 (13,13,13,13,13,13,13,13,13,13,13,13,13,13,13,-91).

Cf. A154638, A169452, A170734.

R:=PowerSeriesRing(Integers(), 40); Coefficients(R!( (1+x)*(1-x^16)/(1-14*x+104*x^16-91*x^17) )); // G. C. Greubel, Sep 10 2023

CoefficientList[Series[(1+t)*(1-t^16)/(1-14*t+104*t^16-91*t^17), {t, 0, 50}], t] (* G. C. Greubel, Jul 01 2016; Sep 10 2023 *)
coxG[{16,91,-13}] (* The coxG program is at A169452 *) (* Harvey P. Dale, Aug 22 2020 *)

def A167955_list(prec):
    P. = PowerSeriesRing(ZZ, prec)
    return P( (1+x)*(1-x^16)/(1-14*x+104*x^16-91*x^17) ).list()
A167955_list(40) # G. C. Greubel, Sep 10 2023

G.f.: (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)/( 91*t^16 - 13*t^15 - 13*t^14 - 13*t^13 - 13*t^12 - 13*t^11 - 13*t^10 - 13*t^9 - 13*t^8 - 13*t^7 - 13*t^6 - 13*t^5 - 13*t^4 - 13*t^3 - 13*t^2 - 13*t + 1).
From G. C. Greubel, Sep 10 2023: (Start)
G.f.: (1+t)*(1-t^16)/(1 - 14*t + 104*t^16 - 91*t^17).
a(n) = 13*Sum_{j=1..15} a(n-j) - 91*a(n-16). (End)

A167924 Number of reduced words of length n in Coxeter group on 16 generators S_i with relations (S_i)^2 = (S_i S_j)^16 = I.

Original entry on oeis.org

1, 16, 240, 3600, 54000, 810000, 12150000, 182250000, 2733750000, 41006250000, 615093750000, 9226406250000, 138396093750000, 2075941406250000, 31139121093750000, 467086816406250000, 7006302246093749880

Offset: 0

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

nonn

The initial terms coincide with those of A170735, although the two sequences are eventually different.

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 (14,14,14,14,14,14,14,14,14,14,14,14,14,14,14,-105).

Cf. A154638, A169452, A170735.

R:=PowerSeriesRing(Integers(), 40); Coefficients(R!( (1+x)*(1-x^16)/(1-15*x+119*x^16-105*x^17) )); // G. C. Greubel, Sep 10 2023

CoefficientList[Series[(1+t)*(1-t^16)/(1-15*t+119*t^16-105*t^17), {t, 0, 50}], t] (* G. C. Greubel, Jul 01 2016; Sep 10 2023 *)
coxG[{16,105,-14}] (* The coxG program is at A169452 *) (* Harvey P. Dale, Jul 10 2017 *)

def A167924_list(prec):
    P. = PowerSeriesRing(ZZ, prec)
    return P( (1+x)*(1-x^16)/(1-15*x+119*x^16-105*x^17) ).list()
A167924_list(40) # G. C. Greubel, Sep 10 2023

G.f.: (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)/( 105*t^16 - 14*t^15 - 14*t^14 - 14*t^13 - 14*t^12 - 14*t^11 - 14*t^10 - 14*t^9 - 14*t^8 - 14*t^7 - 14*t^6 - 14*t^5 - 14*t^4 - 14*t^3 - 14*t^2 - 14*t + 1).
From G. C. Greubel, Sep 10 2023: (Start)
G.f.: (1+t)*(1-t^16)/(1 - 15*t + 119*t^16 - 105*t^17).
a(n) = 14*Sum_{j=1..15} a(n-j) - 105*a(n-16). (End)

cp's OEIS Frontend

A166608 Number of reduced words of length n in Coxeter group on 22 generators S_i with relations (S_i)^2 = (S_i S_j)^12 = I.

Views

Author

Keywords

Comments

Links

Programs

Magma

Mathematica

PARI

Sage

Formula

A166610 Number of reduced words of length n in Coxeter group on 23 generators S_i with relations (S_i)^2 = (S_i S_j)^12 = I.

Views

Author

Keywords

Comments

Links

Programs

Magma

Mathematica

PARI

Sage

Formula

A167882 Number of reduced words of length n in Coxeter group on 4 generators S_i with relations (S_i)^2 = (S_i S_j)^16 = I.

Views

Author

Keywords

Comments

Links

Crossrefs

Programs

Magma

Mathematica

SageMath

Formula

A167896 Number of reduced words of length n in Coxeter group on 5 generators S_i with relations (S_i)^2 = (S_i S_j)^16 = I.

Views

Author

Keywords

Comments

Links

Crossrefs

Programs

Magma

Mathematica

SageMath

Formula

A167900 Number of reduced words of length n in Coxeter group on 9 generators S_i with relations (S_i)^2 = (S_i S_j)^16 = I.

Views

Author

Keywords

Comments

Links

Crossrefs

Programs

Magma

Mathematica

SageMath

Formula

A167908 Number of reduced words of length n in Coxeter group on 10 generators S_i with relations (S_i)^2 = (S_i S_j)^16 = I.

Views

Author

Keywords

Comments

Links

Crossrefs

Programs

Magma

Mathematica

SageMath

Formula

A167914 Number of reduced words of length n in Coxeter group on 11 generators S_i with relations (S_i)^2 = (S_i S_j)^16 = I.

Views

Author

Keywords

Comments

Links

Crossrefs