A003946 -id:A003946 - cp's OEIS frontend

A155118 Array T(n,k) read by antidiagonals: the k-th term of the n-th iterated differences of A140429.

0, 1, 1, 1, 2, 3, 3, 4, 6, 9, 5, 8, 12, 18, 27, 11, 16, 24, 36, 54, 81, 21, 32, 48, 72, 108, 162, 243, 43, 64, 96, 144, 216, 324, 486, 729, 85, 128, 192, 288, 432, 648, 972, 1458, 2187, 171, 256, 384, 576, 864, 1296, 1944, 2916, 4374, 6561, 341, 512, 768, 1152, 1728, 2592, 3888, 5832, 8748, 13122, 19683

Offset: 0

Paul Curtz, Jan 20 2009

Deleting column k=0 and reading by antidiagonals yields A036561.

Deleting column k=0 and reading the antidiagonals downwards yields A175840.

			The array starts in row n=0 with columns k>=0 as:
   0   1    3    9    27    81    243    729    2187  ... A140429;
   1   2    6   18    54   162    486   1458    4374  ... A025192;
   1   4   12   36   108   324    972   2916    8748  ... A003946;
   3   8   24   72   216   648   1944   5832   17496  ... A080923;
   5  16   48  144   432  1296   3888  11664   34992  ... A257970;
  11  32   96  288   864  2592   7776  23328   69984  ...
  21  64  192  576  1728  5184  15552  46656  139968  ...
Antidiagonal triangle begins as:
   0;
   1,   1;
   1,   2,   3;
   3,   4,   6,   9;
   5,   8,  12,  18,  27;
  11,  16,  24,  36,  54,  81;
  21,  32,  48,  72, 108, 162, 243;
  43,  64,  96, 144, 216, 324, 486, 729;
  85, 128, 192, 288, 432, 648, 972, 1458, 2187; - _G. C. Greubel_, Mar 25 2021

Nathaniel Johnston, Table of n, a(n) for n = 0..10000

Cf. A001045, A004054, A046936.

t:= func< n,k | k eq 0 select (2^(n-k) -(-1)^(n-k))/3 else 2^(n-k)*3^(k-1) >;
[t(n,k): k in [0..n], n in [0..12]]; // G. C. Greubel, Mar 25 2021

T:=proc(n,k)if(k>0)then return 2^n*3^(k-1):else return (2^n - (-1)^n)/3:fi:end:
for d from 0 to 8 do for m from 0 to d do print(T(d-m,m)):od:od: # Nathaniel Johnston, Apr 13 2011

t[n_, k_]:= If[k==0, (2^(n-k) -(-1)^(n-k))/3, 2^(n-k)*3^(k-1)];
Table[t[n, k], {n,0,12}, {k,0,n}]//Flatten (* G. C. Greubel, Mar 25 2021 *)

def A155118(n,k): return (2^(n-k) -(-1)^(n-k))/3 if k==0 else 2^(n-k)*3^(k-1)
flatten([[A155118(n,k) for k in (0..n)] for n in (0..12)]) # G. C. Greubel, Mar 25 2021

For the square array:
T(n,k) = 2^n*3^(k-1), k>0.
T(n,k) = T(n-1,k+1) - T(n-1,k), n>0.
Rows:
T(0,k) = A140429(k) = A000244(k-1).
T(1,k) = A025192(k).
T(2,k) = A003946(k).
T(3,k) = A080923(k+1).
T(4,k) = A257970(k+3).
Columns:
T(n,0) = A001045(n) (Jacobsthal numbers J_{n}).
T(n,1) = A000079(n).
T(n,2) = A007283(n).
T(n,3) = A005010(n).
T(n,4) = A175806(n).
T(0,k) - T(k+1,0) = 4*A094705(k-2).
From G. C. Greubel, Mar 25 2021: (Start)
For the antidiagonal triangle:
t(n, k) = T(n-k, k).
t(n, k) = (2^(n-k) - (-1)^(n-k))/3 (J_{n-k}) if k = 0 else 2^(n-k)*3^(k-1).
Sum_{k=0..n} t(n, k) = 3^n - J_{n+1}, where J_{n} = A001045(n).
Sum_{k=0..n} t(n, k) = A004054(n-1) for n >= 1. (End)

a(22) - a(57) from Nathaniel Johnston, Apr 13 2011

A163315 Number of reduced words of length n in Coxeter group on 4 generators S_i with relations (S_i)^2 = (S_i S_j)^5 = I.

Original entry on oeis.org

1, 4, 12, 36, 108, 318, 936, 2760, 8136, 23976, 70662, 208260, 613788, 1808964, 5331420, 15712878, 46309320, 136483800, 402247944, 1185513624, 3493970742, 10297504260, 30349021740, 89445276900, 263615006412, 776931706398

Offset: 0

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

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..1000
Index entries for linear recurrences with constant coefficients, signature (2, 2, 2, 2, -3).

R:=PowerSeriesRing(Integers(), 30); Coefficients(R!( (1+x)*(1-x^5)/(1-3*x+5*x^5-3*x^6) )); // G. C. Greubel, May 12 2019

CoefficientList[Series[(1+x)*(1-x^5)/(1-3*x+5*x^5-3*x^6), {x,0,30}], x] (* or *) Join[{1}, LinearRecurrence[{2,2,2,2,-3}, {1,4,12,36,108,318}, 30]] (* G. C. Greubel, Dec 18 2016 *)
coxG[{4, 3, -2}] (* The coxG program is at A169452 *) (* G. C. Greubel, May 12 2019 *)

my(x='x+O('x^30)); Vec((1+x)*(1-x^5)/(1-3*x+5*x^5-3*x^6)) \\ G. C. Greubel, Dec 18 2016

((1+x)*(1-x^5)/(1-3*x+5*x^5-3*x^6)).series(x, 30).coefficients(x, sparse=False) # G. C. Greubel, May 12 2019

G.f.: (t^5 + 2*t^4 + 2*t^3 + 2*t^2 + 2*t + 1)/(3*t^5 - 2*t^4 - 2*t^3 - 2*t^2 - 2*t + 1).

a(n) = 2*a(n-1)+2*a(n-2)+2*a(n-3)+2*a(n-4)-3*a(n-5). - Wesley Ivan Hurt, May 10 2021

A164353 Number of reduced words of length n in Coxeter group on 4 generators S_i with relations (S_i)^2 = (S_i S_j)^7 = I.

Original entry on oeis.org

1, 4, 12, 36, 108, 324, 972, 2910, 8712, 26088, 78120, 233928, 700488, 2097576, 6281094, 18808452, 56321052, 168650820, 505017180, 1512250884, 4528366236, 13559985966, 40604758920, 121589096856, 364092999624, 1090259865432

Offset: 0

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

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.

Vincenzo Librandi, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (2,2,2,2,2,2,-3).

R:=PowerSeriesRing(Integers(), 30); Coefficients(R!( (1+t)*(1-t^7)/(1-3*t+5*t^7-3*t^8) )); // G. C. Greubel, Aug 24 2019

seq(coeff(series((1+t)*(1-t^7)/(1-3*t+5*t^7-3*t^8), t, n+1), t, n), n = 0 .. 30); # G. C. Greubel, Aug 24 2019

CoefficientList[Series[(x^7 + 2 x^6 + 2 x^5 + 2 x^4 + 2 x^3 + 2 x^2 + 2 x + 1)/(3 x^7 - 2 x^6 - 2 x^5 - 2 x^4 - 2 x^3 - 2 x^2 - 2 x + 1), {x, 0, 40}], x ] (* Vincenzo Librandi, Apr 29 2014 *)
coxG[{7,3,-2,30}] (* The coxG program is at A169452 *) (* Harvey P. Dale, Oct 15 2015 *)

my(t='t+O('t^30)); Vec((1+t)*(1-t^7)/(1-3*t+5*t^7-3*t^8)) \\ G. C. Greubel, Sep 15 2017

def A164353_list(prec):
    P. = PowerSeriesRing(ZZ, prec)
    return P((1+t)*(1-t^7)/(1-3*t+5*t^7-3*t^8)).list()
A164353_list(30) # G. C. Greubel, Aug 24 2019

G.f.: (x^7 + 2*x^6 + 2*x^5 + 2*x^4 + 2*x^3 + 2*x^2 + 2*x + 1)/(3*x^7 - 2*x^6 - 2*x^5 - 2*x^4 - 2*x^3 - 2*x^2 - 2*x + 1).

a(n) = -3*a(n-7) + 2*Sum_{k=1..6} a(n-k). - Wesley Ivan Hurt, May 11 2021

A164697 Number of reduced words of length n in Coxeter group on 4 generators S_i with relations (S_i)^2 = (S_i S_j)^8 = I.

Original entry on oeis.org

1, 4, 12, 36, 108, 324, 972, 2916, 8742, 26208, 78576, 235584, 706320, 2117664, 6349104, 19035648, 57071982, 171111132, 513019140, 1538115228, 4611520836, 13826093148, 41452886916, 124282529820, 372619336494, 1117173669768

Offset: 0

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

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.

Vincenzo Librandi, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (2,2,2,2,2,2,2,-3).

a:=[4, 12, 36, 108, 324, 972, 2916, 8742];; for n in [9..30] do a[n]:=2*Sum([1..7], j-> a[n-j]) -3*a[n-8]; od; Concatenation([1], a); # G. C. Greubel, Sep 16 2019

R:=PowerSeriesRing(Integers(), 30); Coefficients(R!( (1+t)*(1-t^8)/(1-3*t+5*t^8-3*t^9) )); // G. C. Greubel, Sep 16 2019

seq(coeff(series((1+t)*(1-t^8)/(1-3*t+5*t^8-3*t^9), t, n+1), t, n), n = 0..30); # G. C. Greubel, Sep 16 2019

CoefficientList[Series[(x^8 +2x^7 +2x^6 +2x^5 +2x^4 +2x^3 +2x^2 +2x +1)/( 3x^8 -2x^7 -2x^6 -2x^5 -2x^4 -2x^3 -2x^2 -2x +1), {x, 0, 40}], x ] (* Vincenzo Librandi, Apr 29 2014 *)
coxG[{8,3,-2,30}] (* The coxG program is at A169452 *) (* Harvey P. Dale, Jan 03 2019 *)

my(t='t+O('t^30)); Vec((1+t)*(1-t^8)/(1-3*t+5*t^8-3*t^9)) \\ G. C. Greubel, Sep 16 2019

def A164697_list(prec):
    P. = PowerSeriesRing(ZZ, prec)
    return P((1+t)*(1-t^8)/(1-3*t+5*t^8-3*t^9)).list()
A164697_list(30) # G. C. Greubel, Sep 16 2019

G.f.: (x^8 + 2*x^7 + 2*x^6 + 2*x^5 + 2*x^4 + 2*x^3 + 2*x^2 + 2*x + 1)/( 3*x^8 - 2*x^7 - 2*x^6 - 2*x^5 - 2*x^4 - 2*x^3 - 2*x^2 - 2*x + 1).

a(n) = -3*a(n-8) + 2*Sum_{k=1..7} a(n-k). - Wesley Ivan Hurt, May 11 2021

A165756 Number of reduced words of length n in Coxeter group on 4 generators S_i with relations (S_i)^2 = (S_i S_j)^10 = I.

Original entry on oeis.org

1, 4, 12, 36, 108, 324, 972, 2916, 8748, 26244, 78726, 236160, 708432, 2125152, 6375024, 19123776, 57367440, 172090656, 516236976, 1548605952, 4645502958, 13935564252, 41803859076, 125403076764, 376183730628, 1128474698076

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,-3).

a:=[4, 12, 36, 108, 324, 972, 2916, 8748, 26244, 78726];; for n in [11..30] do a[n]:=2*Sum([1..9], j-> a[n-j]) -3*a[n-10]; od; Concatenation([1], a); # G. C. Greubel, Sep 16 2019

R:=PowerSeriesRing(Integers(), 30); Coefficients(R!( (1+t)*(1-t^10)/(1-3*t+5*t^10-3*t^11) )); // G. C. Greubel, Sep 16 2019

seq(coeff(series((1+t)*(1-t^10)/(1-3*t+5*t^10-3*t^11), t, n+1), t, n), n = 0 .. 30); # G. C. Greubel, Sep 16 2019

CoefficientList[Series[(1+t)*(1-t^10)/(1-3*t+5*t^10-3*t^11), {t, 0, 30}], t] (* G. C. Greubel, Apr 07 2016 *)
coxG[{10, 3, -2}] (* The coxG program is at A169452 *) (* G. C. Greubel, Sep 16 2019 *)

my(t='t+O('t^30)); Vec((1+t)*(1-t^10)/(1-3*t+5*t^10-3*t^11)) \\ G. C. Greubel, Sep 16 2019

def A165756_list(prec):
    P. = PowerSeriesRing(ZZ, prec)
    return P((1+t)*(1-t^10)/(1-3*t+5*t^10-3*t^11)).list()
A165756_list(30) # G. C. Greubel, Sep 16 2019

G.f.: (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^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).

A166328 Number of reduced words of length n in Coxeter group on 4 generators S_i with relations (S_i)^2 = (S_i S_j)^11 = I.

Original entry on oeis.org

1, 4, 12, 36, 108, 324, 972, 2916, 8748, 26244, 78732, 236190, 708552, 2125608, 6376680, 19129608, 57387528, 172158696, 516464424, 1549358280, 4647969864, 13943594664, 41829839238, 125486683524, 376451548188, 1129329137988

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..1000
Index entries for linear recurrences with constant coefficients, signature (2,2,2,2,2,2,2,2,2,2,-3).

seq(coeff(series((1+t)*(1-t^11)/(1-3*t+5*t^11-3*t^12), t, n+1), t, n), n = 0..30); # G. C. Greubel, Mar 12 2020

CoefficientList[Series[(1+t)*(1-t^11)/(1-3*t+5*t^11-3*t^12), {t,0,30}], t] (* G. C. Greubel, May 09 2016 *)
coxG[{11, 3, -2}] (* The coxG program is in A169452 *) (* G. C. Greubel, Mar 12 2020 *)

def A166328_list(prec):
    P. = PowerSeriesRing(ZZ, prec)
    return P( (1+t)*(1-t^11)/(1-3*t+5*t^11-3*t^12) ).list()
A166328_list(30) # G. C. Greubel, Aug 10 2019

G.f.: (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^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).

A166858 Number of reduced words of length n in Coxeter group on 4 generators S_i with relations (S_i)^2 = (S_i S_j)^13 = I.

Original entry on oeis.org

1, 4, 12, 36, 108, 324, 972, 2916, 8748, 26244, 78732, 236196, 708588, 2125758, 6377256, 19131720, 57395016, 172184616, 516552552, 1549653768, 4648949640, 13946813928, 41840336808, 125520695496, 376561141704, 1129680590760

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..1000
Index entries for linear recurrences with constant coefficients, signature (2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, -3).

CoefficientList[Series[(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^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), {t, 0, 50}], t] (* G. C. Greubel, May 25 2016 *)
coxG[{13,3,-2,30}] (* The coxG program is at A169452 *) (* Harvey P. Dale, Jul 27 2022 *)

G.f.: (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^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).

A167105 Number of reduced words of length n in Coxeter group on 4 generators S_i with relations (S_i)^2 = (S_i S_j)^14 = I.

Original entry on oeis.org

1, 4, 12, 36, 108, 324, 972, 2916, 8748, 26244, 78732, 236196, 708588, 2125764, 6377286, 19131840, 57395472, 172186272, 516558384, 1549673856, 4649017680, 13947041376, 41841089136, 125523162432, 376569172368, 1129706572320

Offset: 0

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

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, -3).

CoefficientList[Series[(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^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), {t, 0, 50}], t] (* G. C. Greubel, Jun 03 2016 *)
coxG[{14,3,-2,30}] (* The coxG program is at A169452 *) (* Harvey P. Dale, Nov 11 2016 *)

G.f.: (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^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).

A167649 Number of reduced words of length n in Coxeter group on 4 generators S_i with relations (S_i)^2 = (S_i S_j)^15 = I.

Original entry on oeis.org

1, 4, 12, 36, 108, 324, 972, 2916, 8748, 26244, 78732, 236196, 708588, 2125764, 6377292, 19131870, 57395592, 172186728, 516560040, 1549679688, 4649037768, 13947109416, 41841316584, 125523914760, 376571639304, 1129714602984

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, -3).

CoefficientList[Series[(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^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), {t, 0, 50}], t] (* G. C. Greubel, Jun 18 2016 *)

G.f.: (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^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).

A168681 Number of reduced words of length n in Coxeter group on 4 generators S_i with relations (S_i)^2 = (S_i S_j)^17 = I.

Original entry on oeis.org

1, 4, 12, 36, 108, 324, 972, 2916, 8748, 26244, 78732, 236196, 708588, 2125764, 6377292, 19131876, 57395628, 172186878, 516560616, 1549681800, 4649045256, 13947135336, 41841404712, 125524210248, 376572619080, 1129717822248

Offset: 0

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

The initial terms coincide with those of A003946, although the two sequences are eventually different.
First disagreement at index 17: a(17) = 172186878, A003946(17) = 172186884. - Klaus Brockhaus, Mar 30 2011
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 (2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,-3).

Cf. A003946 (G.f.: (1+x)/(1-3*x)).

R:=PowerSeriesRing(Integers(), 40);
Coefficients(R!( (1+t)*(1-t^17)/(1 -3*t +5*t^17 -3*t^18) )); // G. C. Greubel, Feb 22 2021

CoefficientList[Series[(1+t)*(1-t^17)/(1 -3*t +5*t^17 -3*t^18), {t, 0, 40}], t] (* G. C. Greubel, Aug 03 2016, Feb 22 2021 *)
coxG[{17, 3, -2, 40}] (* The coxG program is at A169452 *) (* G. C. Greubel, Feb 22 2021 *)

def A168681_list(prec):
    P. = PowerSeriesRing(ZZ, prec)
    return P( (1+t)*(1-t^17)/(1 -3*t +5*t^17 -3*t^18) ).list()
A168681_list(40) # G. C. Greubel, Feb 22 2021

G.f.: (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)/(3*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).

G.f.: (1+t)*(1-t^17)/(1 -3*t +5*t^17 -3*t^18). - G. C. Greubel, Feb 22 2021

cp's OEIS Frontend

A155118 Array T(n,k) read by antidiagonals: the k-th term of the n-th iterated differences of A140429.

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A163315 Number of reduced words of length n in Coxeter group on 4 generators S_i with relations (S_i)^2 = (S_i S_j)^5 = I.

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A164353 Number of reduced words of length n in Coxeter group on 4 generators S_i with relations (S_i)^2 = (S_i S_j)^7 = I.

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A164697 Number of reduced words of length n in Coxeter group on 4 generators S_i with relations (S_i)^2 = (S_i S_j)^8 = I.

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A165756 Number of reduced words of length n in Coxeter group on 4 generators S_i with relations (S_i)^2 = (S_i S_j)^10 = I.

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A166328 Number of reduced words of length n in Coxeter group on 4 generators S_i with relations (S_i)^2 = (S_i S_j)^11 = I.

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