A169452 -id:A169452 - cp's OEIS frontend

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.

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)

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.

Original entry on oeis.org

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)

cp's OEIS Frontend

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.

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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.

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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.

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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.

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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.

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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.

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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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