A154638 -id:A154638 - cp's OEIS frontend

A167938 Number of reduced words of length n in Coxeter group on 24 generators S_i with relations (S_i)^2 = (S_i S_j)^16 = I.

1, 24, 552, 12696, 292008, 6716184, 154472232, 3552861336, 81715810728, 1879463646744, 43227663875112, 994236269127576, 22867434189934248, 525950986368487704, 12096872686475217192, 278228071788929995416

Offset: 0

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

nonn

The initial terms coincide with those of A170743, 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 (22,22,22,22,22,22,22,22,22,22,22,22,22,22,22,-253).

Cf. A154638, A167881, A169452, A170758.

R:=PowerSeriesRing(Integers(), 40); Coefficients(R!( (1+x)*(1-x^16)/(1-23*x+275*x^16-253*x^17) )); // G. C. Greubel, Sep 09 2023

CoefficientList[Series[(1+t)*(1-t^16)/(1-23*t+275*t^16-253*t^17), {t, 0, 50}], t] (* G. C. Greubel, Jul 01 2016; Sep 09 2023 *)
coxG[{16,253,-22}] (* The coxG program is at A169452 *) (* Harvey P. Dale, Mar 18 2022 *)

def A167938_list(prec):
    P. = PowerSeriesRing(ZZ, prec)
    return P( (1+x)*(1-x^16)/(1-23*x+275*x^16-253*x^17) ).list()
A167938_list(40) # G. C. Greubel, Sep 09 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)/( 253*t^16 - 22*t^15 - 22*t^14 - 22*t^13 - 22*t^12 - 22*t^11 - 22*t^10 - 22*t^9 - 22*t^8 - 22*t^7 - 22*t^6 - 22*t^5 - 22*t^4 - 22*t^3 - 22*t^2 - 22*t + 1).
From G. C. Greubel, Sep 09 2023: (Start)
G.f.: (1+t)*(1-t^16)/(1 - 23*t + 275*t^16 - 253*t^17).
a(n) = 22*Sum_{j=1..15} a(n-j) - 253*a(n-16). (End)

A167940 Number of reduced words of length n in Coxeter group on 25 generators S_i with relations (S_i)^2 = (S_i S_j)^16 = 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.

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 (23,23,23,23,23,23,23,23,23,23,23,23,23,23,23,-276).

Cf. A154638, A169452, A170758.

R:=PowerSeriesRing(Integers(), 40); Coefficients(R!( (1+x)*(1-x^16)/(1-24*x+299*x^16-276*x^17) )); // G. C. Greubel, Sep 08 2023

coxG[{16,276,-23}] (* The coxG program is at A169452 *) (* Harvey P. Dale, May 05 2015 *)
CoefficientList[Series[(1+t)*(1-t^16)/(1-24*t+299*t^16-276*t^17), {t, 0, 50}], t] (* G. C. Greubel, Jul 01 2016; Sep 08 2023 *)

def A167940_list(prec):
    P. = PowerSeriesRing(ZZ, prec)
    return P( (1+x)*(1-x^16)/(1-24*x+299*x^16-276*x^17) ).list()
A167940_list(40) # G. C. Greubel, Sep 08 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)/( 276*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).
From G. C. Greubel, Sep 08 2023: (Start)
G.f.: (1+t)*(1-t^16)/(1 - 24*t + 299*t^16 - 276*t^17).
a(n) = 23*Sum_{j=1..15} a(n-j) - 276*a(n-16). (End)

A167947 Number of reduced words of length n in Coxeter group on 32 generators S_i with relations (S_i)^2 = (S_i S_j)^16 = I.

Original entry on oeis.org

1, 32, 992, 30752, 953312, 29552672, 916132832, 28400117792, 880403651552, 27292513198112, 846067909141472, 26228105183385632, 813071260684954592, 25205209081233592352, 781361481518241362912, 24222205927065482250272

Offset: 0

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

nonn

The initial terms coincide with those of A170751, 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 (30,30,30,30,30,30,30,30,30,30,30,30,30,30,30,-465).

Cf. A154638, A169452, A170751.

R:=PowerSeriesRing(Integers(), 40); Coefficients(R!( (1+x)*(1-x^16)/(1-31*x+495*x^16-465*x^17) )); // G. C. Greubel, Sep 07 2023

coxG[{16,465,-30}] (* The coxG program is at A169452 *) (* Harvey P. Dale, Apr 16 2015 *)
CoefficientList[Series[(1+t)*(1-t^16)/(1-31*t+495*t^16-465*t^17), {t, 0, 50}], t] (* G. C. Greubel, Jul 02 2016; Sep 07 2023 *)

def A167947_list(prec):
    P. = PowerSeriesRing(ZZ, prec)
    return P( (1+x)*(1-x^16)/(1-31*x+495*x^16-465*x^17) ).list()
A167947_list(40) # G. C. Greubel, Sep 07 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)/( 465*t^16 - 30*t^15 - 30*t^14 - 30*t^13 - 30*t^12 - 30*t^11 - 30*t^10 - 30*t^9 - 30*t^8 - 30*t^7 - 30*t^6 - 30*t^5 - 30*t^4 - 30*t^3 - 30*t^2 - 30*t + 1).
From G. C. Greubel, Sep 07 2023: (Start)
G.f.: (1+t)*(1-t^16)/(1 - 31*t + 495*t^16 - 465*t^17).
a(n) = 30*Sum_{j=1..15} a(n-j) - 465*a(n-16). (End)

A167949 Number of reduced words of length n in Coxeter group on 33 generators S_i with relations (S_i)^2 = (S_i S_j)^16 = I.

Original entry on oeis.org

1, 33, 1056, 33792, 1081344, 34603008, 1107296256, 35433480192, 1133871366144, 36283883716608, 1161084278931456, 37154696925806592, 1188950301625810944, 38046409652025950208, 1217485108864830406656, 38959523483674573012992

Offset: 0

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

nonn

The initial terms coincide with those of A170752, 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 (31,31,31,31,31,31,31,31,31,31,31,31,31,31,31,-496).

Cf. A154638, A169452, A170752.

R:=PowerSeriesRing(Integers(), 40); Coefficients(R!( (1+x)*(1-x^16)/(1-32*x+527*x^16-496*x^17) )); // G. C. Greubel, Sep 07 2023

CoefficientList[Series[(1+t)*(1-t^16)/(1-32*t+527*t^16-496*t^17), {t, 0, 50}], t] (* G. C. Greubel, Jul 02 2016; Sep 07 2023 *)
coxG[{16,496,-31}] (* The coxG program is at A169452 *) (* Harvey P. Dale, Sep 22 2020 *)

def A167949_list(prec):
    P. = PowerSeriesRing(ZZ, prec)
    return P( (1+x)*(1-x^16)/(1-32*x+527*x^16-496*x^17) ).list()
A167949_list(40) # G. C. Greubel, Sep 07 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)/( 496*t^16 - 31*t^15 - 31*t^14 - 31*t^13 - 31*t^12 - 31*t^11 - 31*t^10 - 31*t^9 - 31*t^8 - 31*t^7 - 31*t^6 - 31*t^5 - 31*t^4 - 31*t^3 - 31*t^2 - 31*t + 1).
From G. C. Greubel, Sep 07 2023: (Start)
G.f.: (1+t)*(1-t^16)/(1 - 32*t + 527*t^16 - 496*t^17).
a(n) = 31*Sum_{j=1..15} a(n-j) - 496*a(n-16). (End)

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.

Original entry on oeis.org

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)

A154636 a(n) is the ratio of the sum of the bends of the circles that are drawn in the n-th generation of Apollonian packing to the sum of the bends of the circles in the initial configuration of 3 circles.

Original entry on oeis.org

1, 2, 18, 138, 1050, 7986, 60738, 461946, 3513354, 26720994, 203227890, 1545660138, 11755597434, 89407799058, 679995600162, 5171741404122, 39333944432490, 299156331247554, 2275248816682962, 17304521539721034, 131610425867719386, 1000969842322591986

Offset: 0

Colin Mallows, Jan 13 2009

For comments and more references and links, see A189226.

			Starting from three circles with bends -1,2,2 summing to 3, the first derived generation consists of two circles, each with bend 3. So a(1) is (3+3)/3 = 2.

Colin Barker, Table of n, a(n) for n = 0..1000
C. L. Mallows, Growing Apollonian Packings, J. Integer Sequences, 12 (2009), article 09.2.1.
Index entries for linear recurrences with constant coefficients, signature (8,-3).

Other sequences relating to the two-dimensional case are A135849, A137246, A154637. For the three-dim. case see A154638 - A154645. Five dimensions: A154635.

Cf. also A189226, A189227.

CoefficientList[Series[(5 z^2 - 6 z + 1)/(3 z^2 - 8 z + 1), {z, 0, 100}], z] (* and *) LinearRecurrence[{8, -3}, {1, 2, 18}, 100] (* Vladimir Joseph Stephan Orlovsky, Jul 03 2011 *)

Vec((1 - x)*(1 - 5*x) / (1 - 8*x + 3*x^2) + O(x^30)) \\ Colin Barker, Jul 15 2017

G.f.: (1 - x)*(1 - 5*x) / (1 - 8*x + 3*x^2).
From Colin Barker, Jul 15 2017: (Start)
a(n) = ((-(-7+sqrt(13))*(4+sqrt(13))^n - (4-sqrt(13))^n*(7+sqrt(13)))) / (3*sqrt(13)) for n>0.
a(n) = 8*a(n-1) - 3*a(n-2) for n>2.
(End)

More terms from N. J. A. Sloane, Nov 22 2009

cp's OEIS Frontend

A167938 Number of reduced words of length n in Coxeter group on 24 generators S_i with relations (S_i)^2 = (S_i S_j)^16 = I.

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A167940 Number of reduced words of length n in Coxeter group on 25 generators S_i with relations (S_i)^2 = (S_i S_j)^16 = I.

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A167947 Number of reduced words of length n in Coxeter group on 32 generators S_i with relations (S_i)^2 = (S_i S_j)^16 = I.

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A167949 Number of reduced words of length n in Coxeter group on 33 generators S_i with relations (S_i)^2 = (S_i S_j)^16 = I.

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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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