A169452 -id:A169452 - cp's OEIS frontend

A167962 Number of reduced words of length n in Coxeter group on 46 generators S_i with relations (S_i)^2 = (S_i S_j)^16 = I.

1, 46, 2070, 93150, 4191750, 188628750, 8488293750, 381973218750, 17188794843750, 773495767968750, 34807309558593750, 1566328930136718750, 70484801856152343750, 3171816083526855468750, 142731723758708496093750

Offset: 0

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

nonn

The initial terms coincide with those of A170765, 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 (44,44,44,44,44,44,44,44,44,44,44,44,44,44,44,-990).

Cf. A154638, A169452, A170765.

R:=PowerSeriesRing(Integers(), 40); Coefficients(R!( (1+x)*(1-x^16)/(1-45*x+1034*x^16-990*x^17) )); // G. C. Greubel, Jan 17 2023

CoefficientList[Series[(1+t)*(1-t^16)/(1-45*t+1034*t^16-990*t^17), {t, 0, 50}], t] (* G. C. Greubel, Jul 03 2016 *)
coxG[{16,990,-44,40}] (* The coxG program is at A169452 *) (* G. C. Greubel, Jan 17 2023 *)

def A167962_list(prec):
    P. = PowerSeriesRing(ZZ, prec)
    return P( (1+x)*(1-x^16)/(1-45*x+1034*x^16-990*x^17) ).list()
A167962_list(40) # G. C. Greubel, Jan 17 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)/( 990*t^16 - 44*t^15 - 44*t^14 - 44*t^13 - 44*t^12 - 44*t^11 - 44*t^10 - 44*t^9 - 44*t^8 - 44*t^7 - 44*t^6 - 44*t^5 - 44*t^4 - 44*t^3 - 44*t^2 - 44*t + 1).
From G. C. Greubel, Jan 17 2023: (Start)
a(n) = Sum_{j=1..15} a(n-j) - 990*a(n-16).
G.f.: (1+x)*(1-x^16)/(1 - 45*x + 1034*x^16 - 990*x^17). (End)

A167978 Number of reduced words of length n in Coxeter group on 47 generators S_i with relations (S_i)^2 = (S_i S_j)^16 = I.

Original entry on oeis.org

1, 47, 2162, 99452, 4574792, 210440432, 9680259872, 445291954112, 20483429889152, 942237774900992, 43342937645445632, 1993775131690499072, 91713656057762957312, 4218828178657096036352, 194066096218226417672192

Offset: 0

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

nonn

The initial terms coincide with those of A170766, 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 (45,45,45,45,45,45,45,45,45,45,45,45,45,45,45,-1035).

Cf. A154638, A169452, A170766.

R:=PowerSeriesRing(Integers(), 30); Coefficients(R!( (1+x)*(1-x^17)/(1-46*x+1081*x^16-1035*x^17) )); // G. C. Greubel, Jan 17 2023

CoefficientList[Series[(1+t)*(1-t^16)/(1-46*t+1081*t^16-1035*t^17), {t, 0,50}], t] (* G. C. Greubel, Jul 03 2016; Jan 17 2023 *)
coxG[{16,1035,-45}] (* The coxG program is at A169452 *) (* G. C. Greubel, Jan 17 2023 *)

def A167978_list(prec):
    P. = PowerSeriesRing(ZZ, prec)
    return P( (1+x)*(1-x^17)/(1-46*x+1081*x^16-1035*x^17) ).list()
A167978_list(30) # G. C. Greubel, Jan 17 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)/( 1035*t^16 - 45*t^15 - 45*t^14 - 45*t^13 - 45*t^12 - 45*t^11 - 45*t^10 - 45*t^9 - 45*t^8 - 45*t^7 - 45*t^6 - 45*t^5 - 45*t^4 - 45*t^3 - 45*t^2 - 45*t + 1).
From G. C. Greubel, Jan 17 2023: (Start)
a(n) = Sum_{j=1..15} a(n-j) - 1035*a(n-16).
G.f.: (1+x)*(1-x^16)/(1 - 46*x + 1081*x^16 - 1035*x^17). (End)

A167980 Number of reduced words of length n in Coxeter group on 48 generators S_i with relations (S_i)^2 = (S_i S_j)^16 = I.

Original entry on oeis.org

1, 48, 2256, 106032, 4983504, 234224688, 11008560336, 517402335792, 24317909782224, 1142941759764528, 53718262708932816, 2524758347319842352, 118663642324032590544, 5577191189229531755568, 262127985893787992511696

Offset: 0

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

nonn

The initial terms coincide with those of A170767, 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 (46,46,46,46,46,46,46,46,46,46,46,46,46,46,46,-1081).

Cf. A154638, A169452, A170767.

R:=PowerSeriesRing(Integers(), 30); Coefficients(R!( (1+x)*(1-x^17)/(1-47*x+1127*x^16-1081*x^17) )); // G. C. Greubel, Jan 17 2023

coxG[{16,1081,-46}] (* The coxG program is at A169452 *) (* Harvey P. Dale, Jun 12 2016 *)
CoefficientList[Series[(1+t)*(1-t^17)/(1-47*t+1127*t^16-1081*t^17), {t, 0,50}], t] (* G. C. Greubel, Jul 03 2016; Jan 17 2023 *)

def A167980_list(prec):
    P. = PowerSeriesRing(ZZ, prec)
    return P( (1+x)*(1-x^17)/(1-47*x+1127*x^16-1081*x^17) ).list()
A167980_list(30) # G. C. Greubel, Jan 17 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)/( 1081*t^16 - 46*t^15 - 46*t^14 - 46*t^13 - 46*t^12 - 46*t^11 - 46*t^10 - 46*t^9 - 46*t^8 - 46*t^7 - 46*t^6 - 46*t^5 - 46*t^4 - 46*t^3 - 46*t^2 - 46*t + 1).
From G. C. Greubel, Jan 17 2023: (Start)
a(n) = Sum_{j=1..15} a(n-j) - 1081*a(n-16).
G.f.: (1+x)*(1-x^17)/(1 - 47*x + 1127*x^16 - 1081*x^17). (End)

A167988 Number of reduced words of length n in Coxeter group on 49 generators S_i with relations (S_i)^2 = (S_i S_j)^16 = I.

Original entry on oeis.org

1, 49, 2352, 112896, 5419008, 260112384, 12485394432, 599298932736, 28766348771328, 1380784741023744, 66277667569139712, 3181328043318706176, 152703746079297896448, 7329779811806299029504, 351829430966702353416192

Offset: 0

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

nonn

The initial terms coincide with those of A170768, 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 (47,47,47,47,47,47,47,47,47,47,47,47,47,47,47,-1128).

Cf. A154638, A169452, A170768.

R:=PowerSeriesRing(Integers(), 40); Coefficients(R!( (1+x)*(1-x^16)/(1-48*x+1175*x^16-1128*x^17) )); // G. C. Greubel, Jan 14 2023

coxG[{16,1128,-47}] (* The coxG program is at A169452 *) (* Harvey P. Dale, May 05 2015 *)
CoefficientList[Series[(1+x)*(1-x^16)/(1-48*x+1175*x^16-1128*x^17), {x, 0, 50}], x] (* G. C. Greubel, Jul 03 2016; Jan 14 2023 *)

def A167988_list(prec):
    P. = PowerSeriesRing(ZZ, prec)
    return P( (1+x)*(1-x^16)/(1-48*x+1175*x^16-1128*x^17) ).list()
A167988_list(40) # G. C. Greubel, Jan 14 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)/( 1128*t^16 - 47*t^15 - 47*t^14 - 47*t^13 - 47*t^12 - 47*t^11 - 47*t^10 - 47*t^9 - 47*t^8 - 47*t^7 - 47*t^6 - 47*t^5 - 47*t^4 - 47*t^3 - 47*t^2 - 47*t + 1).
From G. C. Greubel, Jan 14 2023: (Start)
a(n) = -1128*a(n-16) + 47*Sum_{j=1..15} a(n-j).
G.f.: (1 + x)*(1 - x^16)/(1 - 48*x + 1175*x^16 - 1128*x^17). (End)

A167989 Number of reduced words of length n in Coxeter group on 50 generators S_i with relations (S_i)^2 = (S_i S_j)^16 = I.

Original entry on oeis.org

1, 50, 2450, 120050, 5882450, 288240050, 14123762450, 692064360050, 33911153642450, 1661646528480050, 81420679895522450, 3989613314880600050, 195491052429149402450, 9579061569028320720050, 469374016882387715282450

Offset: 0

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

nonn

The initial terms coincide with those of A170769, 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 (48,48,48,48,48,48,48,48,48,48,48,48,48,48,48,-1176).

Cf. A154638, A169452, A170769.

R:=PowerSeriesRing(Integers(), 40); Coefficients(R!( (1+x)*(1-x^16)/(1-49*x+1224*x^16-1176*x^17) )); // G. C. Greubel, Jan 14 2023

CoefficientList[Series[(1+x)*(1-x^16)/(1-49*x+1224*x^16-1176*x^17), {x, 0, 50}], x] (* G. C. Greubel, Jul 03 2016; Jan 14 2023 *)
coxG[{16, 1176, -48, 10}] (* The coxG program is at A169452 *) (* G. C. Greubel, Jan 14 2023 *)

def A167989_list(prec):
    P. = PowerSeriesRing(ZZ, prec)
    return P( (1+x)*(1-x^16)/(1-49*x+1224*x^16-1176*x^17) ).list()
A167989_list(40) # G. C. Greubel, Jan 14 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)/( 1176*t^16 - 48*t^15 - 48*t^14 - 48*t^13 - 48*t^12 - 48*t^11 - 48*t^10 - 48*t^9 - 48*t^8 - 48*t^7 - 48*t^6 - 48*t^5 - 48*t^4 - 48*t^3 - 48*t^2 - 48*t + 1).
From G. C. Greubel, Jan 14 2023: (Start)
a(n) = -1176*a(n-16) + 48*Sum_{j=1..15} a(n-j).
G.f.: (1+x)*(1-x^16)/(1-49*x+1224*x^16-1176*x^17). (End)

A167919 Number of reduced words of length n in Coxeter group on 13 generators S_i with relations (S_i)^2 = (S_i S_j)^16 = I.

Original entry on oeis.org

1, 13, 156, 1872, 22464, 269568, 3234816, 38817792, 465813504, 5589762048, 67077144576, 804925734912, 9659108818944, 115909305827328, 1390911669927936, 16690940039135232, 200291280469622706

Offset: 0

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

nonn

The initial terms coincide with those of A170732, 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 (11,11,11,11,11,11,11,11,11,11,11,11,11,11,11,-66).

Cf. A154638, A169452, A170732.

Cf. A167881, A167882, A167896 - A167900, A167908, A167914, A167916, A167922, A167923, A167924, A167926, A167927, A167929, A167931, A167933, A167935, A167937, A167938, A167940 - A167947, A167949 - A167962, A167978, A167980, A167988, A167989.

R:=PowerSeriesRing(Integers(), 40); Coefficients(R!( (1+x)*(1-x^16)/(1-12*x+77*x^16-66*x^17) )); // G. C. Greubel, Sep 13 2023

CoefficientList[Series[(1+t)*(1-t^16)/(1-12*t+77*t^16-66*t^17), {t, 0, 50}], t] (* G. C. Greubel, Jul 01 2016; Sep 13 2023 *)
coxG[{16,66,-11}] (* The coxG program is at A169452 *) (* Harvey P. Dale, Mar 28 2018 *)

def A167919_list(prec):
    P. = PowerSeriesRing(ZZ, prec)
    return P( (1+x)*(1-x^16)/(1-12*x+77*x^16-66*x^17) ).list()
A167919_list(40) # G. C. Greubel, Sep 13 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)/( 66*t^16 - 11*t^15 - 11*t^14 - 11*t^13 - 11*t^12 - 11*t^11 - 11*t^10 - 11*t^9 - 11*t^8 - 11*t^7 - 11*t^6 - 11*t^5 - 11*t^4 - 11*t^3 - 11*t^2 - 11*t + 1).
From G. C. Greubel, Sep 13 2023: (Start)
G.f.: (1+t)*(1-t^16)/(1 - 12*t + 77*t^16 - 66*t^17).
a(n) = 11*Sum_{j=1..15} a(n-j) - 66*a(n-16). (End)

A167922 Number of reduced words of length n in Coxeter group on 14 generators S_i with relations (S_i)^2 = (S_i S_j)^16 = I.

Original entry on oeis.org

1, 14, 182, 2366, 30758, 399854, 5198102, 67575326, 878479238, 11420230094, 148462991222, 1930018885886, 25090245516518, 326173191714734, 4240251492291542, 55123269399790046, 716602502197270507

Offset: 0

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

nonn

The initial terms coincide with those of A170733, 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 (12,12,12,12,12,12,12,12,12,12,12,12,12,12,12,-78).

Cf. A154638, A169452, A170733.

Cf. A167881, A167882, A167896 - A167900, A167908, A167914, A167916, A167919, A167923, A167924, A167926, A167927, A167929, A167931, A167933, A167935, A167937, A167938, A167940 - A167947, A167949 - A167962, A167978, A167980, A167988, A167989.

R:=PowerSeriesRing(Integers(), 40); Coefficients(R!( (1+x)*(1-x^16)/(1-13*x+90*x^16-78*x^17) )); // G. C. Greubel, Sep 13 2023

CoefficientList[Series[(1+t)*(1-t^16)/(1-13*t+90*t^16-78*t^17), {t, 0, 50}], t] (* G. C. Greubel, Jul 01 2016; Sep 13 2023 *)
coxG[{16, 78, -12, 40}] (* The coxG program is at A169452 *) (* G. C. Greubel, Sep 13 2023 *)

def A167922_list(prec):
    P. = PowerSeriesRing(ZZ, prec)
    return P( (1+x)*(1-x^16)/(1-13*x+90*x^16-78*x^17) ).list()
A167922_list(40) # G. C. Greubel, Sep 13 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)/( 78*t^16 - 12*t^15 - 12*t^14 - 12*t^13 - 12*t^12 - 12*t^11 - 12*t^10 - 12*t^9 - 12*t^8 - 12*t^7 - 12*t^6 - 12*t^5 - 12*t^4 - 12*t^3 - 12*t^2 - 12*t + 1).
From G. C. Greubel, Sep 13 2023: (Start)
G.f.: (1+t)*(1-t^16)/(1 - 13*t + 90*t^16 - 78*t^17).
a(n) = 12*Sum_{j=1..15} a(n-j) - 78*a(n-16). (End)

A167926 Number of reduced words of length n in Coxeter group on 17 generators S_i with relations (S_i)^2 = (S_i S_j)^16 = I.

Original entry on oeis.org

1, 17, 272, 4352, 69632, 1114112, 17825792, 285212672, 4563402752, 73014444032, 1168231104512, 18691697672192, 299067162755072, 4785074604081152, 76561193665298432, 1224979098644774912, 19599665578316398456

Offset: 0

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

nonn

The initial terms coincide with those of A170736, 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 (15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,-120).

Cf. A154638, A169452, A170736.

Cf. A167881, A167882, A167896 - A167900, A167908, A167914, A167916, A167919, A167922, A167923, A167924, A167927, A167929, A167931, A167933, A167935, A167937, A167938, A167940 - A167947, A167949 - A167962, A167978, A167980, A167988, A167989.

R:=PowerSeriesRing(Integers(), 40); Coefficients(R!( (1+x)*(1-x^16)/(1-16*x+135*x^16-120*x^17) )); // G. C. Greubel, Sep 10 2023

coxG[{16,120,-15}] (* The coxG program is at A169452 *) (* Harvey P. Dale, Nov 27 2015 *)
CoefficientList[Series[(1+t)*(1-t^16)/(1-16*t+135*t^16-120*t^17), {t, 0, 50}], t] (* G. C. Greubel, Jul 01 2016; Sep 10 2023 *)

def A167926_list(prec):
    P. = PowerSeriesRing(ZZ, prec)
    return P( (1+x)*(1-x^16)/(1-16*x+135*x^16-120*x^17) ).list()
A167926_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)/( 120*t^16 - 15*t^15 - 15*t^14 - 15*t^13 - 15*t^12 - 15*t^11 - 15*t^10 - 15*t^9 - 15*t^8 - 15*t^7 - 15*t^6 - 15*t^5 - 15*t^4 - 15*t^3 - 15*t^2 - 15*t + 1).
From G. C. Greubel, Sep 10 2023: (Start)
G.f.: (1+t)*(1-t^16)/(1 - 16*t + 135*t^16 - 120*t^17).
a(n) = 15*Sum_{j=1..15} a(n-j) - 120*a(n-16). (End)

A167927 Number of reduced words of length n in Coxeter group on 18 generators S_i with relations (S_i)^2 = (S_i S_j)^16 = I.

Original entry on oeis.org

1, 18, 306, 5202, 88434, 1503378, 25557426, 434476242, 7386096114, 125563633938, 2134581776946, 36287890208082, 616894133537394, 10487200270135698, 178282404592306866, 3030800878069216722, 51523614927176684121

Offset: 0

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

nonn

The initial terms coincide with those of A170737, 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 (16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,-136).

Cf. A154638, A169452, A170737.

Cf. A167881, A167882, A167896 - A167900, A167908, A167914, A167916, A167919, A167922, A167923, A167924, A167926, A167929, A167931, A167933, A167935, A167937, A167938, A167940 - A167947, A167949 - A167962, A167978, A167980, A167988, A167989.

R:=PowerSeriesRing(Integers(), 40); Coefficients(R!( (1+x)*(1-x^16)/(1-17*x+152*x^16-136*x^17) )); // G. C. Greubel, Sep 10 2023

CoefficientList[Series[(1+t)*(1-t^16)/(1-17*t+152*t^16-136*t^17), {t, 0, 50}], t] (* G. C. Greubel, Jul 01 2016; Sep 10 2023 *)
coxG[{16,136,-16}] (* The coxG program is at A169452 *) (* Harvey P. Dale, May 15 2022 *)

def A167927_list(prec):
    P. = PowerSeriesRing(ZZ, prec)
    return P( (1+x)*(1-x^16)/(1-17*x+152*x^16-136*x^17) ).list()
A167927_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)/( 136*t^16 - 16*t^15 - 16*t^14 - 16*t^13 - 16*t^12 - 16*t^11 - 16*t^10 - 16*t^9 - 16*t^8 - 16*t^7 - 16*t^6 - 16*t^5 - 16*t^4 - 16*t^3 - 16*t^2 - 16*t + 1).
From G. C. Greubel, Sep 10 2023: (Start)
G.f.: (1+t)*(1-t^16)/(1 - 17*t + 152*t^16 - 136*t^17).
a(n) = 16*Sum_{j=1..15} a(n-j) - 136*a(n-16). (End)

A167937 Number of reduced words of length n in Coxeter group on 23 generators S_i with relations (S_i)^2 = (S_i S_j)^16 = I.

Original entry on oeis.org

1, 23, 506, 11132, 244904, 5387888, 118533536, 2607737792, 57370231424, 1262145091328, 27767192009216, 610878224202752, 13439320932460544, 295665060514131968, 6504631331310903296, 143101889288839872512

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

Cf. A154638, A169452, A170742.

Cf. A167881, A167882, A167896 - A167900, A167908, A167914, A167916, A167919, A167922, A167923, A167924, A167926, A167927, A167929, A167931, A167933, A167935, A167938, A167940 - A167947, A167949 - A167962, A167978, A167980, A167988, A167989.

R:=PowerSeriesRing(Integers(), 40); Coefficients(R!( (1+x)*(1-x^16)/(1-22*x+252*x^16-231*x^17) )); // G. C. Greubel, Sep 10 2023

CoefficientList[Series[(1+t)*(1-t^16)/(1-22*t+252*t^16-231*t^17), {t, 0, 50}], t] (* G. C. Greubel, Jul 01 2016; Sep 10 2023 *)
coxG[{16,231,-21}] (* The coxG program is at A169452 *) (* Harvey P. Dale, Dec 27 2016 *)

def A167937_list(prec):
    P. = PowerSeriesRing(ZZ, prec)
    return P( (1+x)*(1-x^16)/(1-22*x+252*x^16-231*x^17) ).list()
A167937_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)/( 231*t^16 - 21*t^15 - 21*t^14 - 21*t^13 - 21*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).
From G. C. Greubel, Sep 10 2023: (Start)
G.f.: (1+t)*(1-t^16)/(1 - 22*t + 252*t^16 - 231*t^17).
a(n) = 21*Sum_{j=1..15} a(n-j) - 231*a(n-16). (End)

cp's OEIS Frontend

A167962 Number of reduced words of length n in Coxeter group on 46 generators S_i with relations (S_i)^2 = (S_i S_j)^16 = I.

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A167978 Number of reduced words of length n in Coxeter group on 47 generators S_i with relations (S_i)^2 = (S_i S_j)^16 = I.

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A167980 Number of reduced words of length n in Coxeter group on 48 generators S_i with relations (S_i)^2 = (S_i S_j)^16 = I.

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A167988 Number of reduced words of length n in Coxeter group on 49 generators S_i with relations (S_i)^2 = (S_i S_j)^16 = I.

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A167989 Number of reduced words of length n in Coxeter group on 50 generators S_i with relations (S_i)^2 = (S_i S_j)^16 = I.

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A167919 Number of reduced words of length n in Coxeter group on 13 generators S_i with relations (S_i)^2 = (S_i S_j)^16 = I.

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A167922 Number of reduced words of length n in Coxeter group on 14 generators S_i with relations (S_i)^2 = (S_i S_j)^16 = I.

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