A170738 -id:A170738 - cp's OEIS frontend

A003945 Expansion of g.f. (1+x)/(1-2*x).

1, 3, 6, 12, 24, 48, 96, 192, 384, 768, 1536, 3072, 6144, 12288, 24576, 49152, 98304, 196608, 393216, 786432, 1572864, 3145728, 6291456, 12582912, 25165824, 50331648, 100663296, 201326592, 402653184, 805306368, 1610612736, 3221225472, 6442450944, 12884901888

Offset: 0

N. J. A. Sloane

Coordination sequence for infinite tree with valency 3.
Number of Hamiltonian cycles in K_3 X P_n.
Number of ternary words of length n avoiding aa, bb, cc.
For n > 0, row sums of A029635. - Paul Barry, Jan 30 2005
Binomial transform is {1, 4, 13, 40, 121, 364, ...}, see A003462. - Philippe Deléham, Jul 23 2005
Convolved with the Jacobsthal sequence A001045 = A001786: (1, 4, 12, 32, 80, ...). - Gary W. Adamson, May 23 2009
Equals (n+1)-th row sums of triangle A161175. - Gary W. Adamson, Jun 05 2009
a(n) written in base 2: a(0) = 1, a(n) for n >= 1: 11, 110, 11000, 110000, ..., i.e.: 2 times 1, (n-1) times 0 (see A003953(n)). - Jaroslav Krizek, Aug 17 2009
INVERTi transform of A003688. - Gary W. Adamson, Aug 05 2010
An elephant sequence, see A175655. For the central square four A[5] vectors, with decimal values 42, 138, 162 and 168, lead to this sequence. For the corner squares these vectors lead to the companion sequence A083329. - Johannes W. Meijer, Aug 15 2010
A216022(a(n)) != 2 and A216059(a(n)) != 3. - Reinhard Zumkeller, Sep 01 2012
Number of length-n strings of 3 letters with no two adjacent letters identical. The general case (strings of r letters) is the sequence with g.f. (1+x)/(1-(r-1)*x). - Joerg Arndt, Oct 11 2012
Sums of pairs of rows of Pascal's triangle A007318, T(2n,k)+T(2n+1,k); Sum_{n>=1} A000290(n)/a(n) = 4. - John Molokach, Sep 26 2013

Vincenzo Librandi, Table of n, a(n) for n = 0..1000
Yasemin Alp and E. Gokcen Kocer, Exponential Almost-Riordan Arrays, Results Math. (2024) Vol. 79, 173.
F. Faase, Counting Hamiltonian cycles in product graphs
INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 151
INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 304
Markus Kuba and Alois Panholzer, Enumeration formulas for pattern restricted Stirling permutations, Discrete Math. 312 (2012), no. 21, 3179--3194. MR2957938. - From _N. J. A. Sloane_, Sep 25 2012
C. Richard and U. Grimm, On the entropy and letter frequencies of ternary squarefree words, arXiv:math/0302302 [math.CO], 2003.
Index to divisibility sequences
Index entries for linear recurrences with constant coefficients, signature (2).
Index entries for sequences related to trees

Essentially same as A007283 (3*2^n) and A042950.
Cf. A001787, A001045, A161175.
Generating functions of the form (1+x)/(1-k*x) for k=1 to 12: A040000, A003945, A003946, A003947, A003948, A003949, A003950, A003951, A003952.
Generating functions of the form (1+x)/(1-k*x) for k=13 to 30: A170732, A170733, A170734, A170735, A170736, A170737, A170738, A170739, A170740, A170741, A170742, A170743, A170744, A170745, A170746, A170747, A170748.
Generating functions of the form (1+x)/(1-k*x) for k=31 to 50: A170749, A170750, A170751, A170752, A170753, A170754, A170755, A170756, A170757, A170758, A170759, A170760, A170761, A170762, A170763, A170764, A170765, A170766, A170767, A170768, A170769.
Cf. A003688.

k := 3; if n = 0 then 1 else k*(k-1)^(n-1); fi;

Join[{1}, 3*2^Range[0, 60]] (* Vladimir Joseph Stephan Orlovsky, Jun 09 2011 *)
Table[2^n+Floor[2^(n-1)], {n,0,30}] (* Martin Grymel, Oct 17 2012 *)
CoefficientList[Series[(1+x)/(1-2x),{x,0,40}],x] (* or *) LinearRecurrence[ {2},{1,3},40] (* Harvey P. Dale, May 04 2017 *)

a(n)=if(n,3<Charles R Greathouse IV, Jan 12 2012

a(0) = 1; for n > 0, a(n) = 3*2^(n-1).
a(n) = 2*a(n-1), n > 1; a(0)=1, a(1)=3.
More generally, the g.f. (1+x)/(1-k*x) produces the sequence [1, 1 + k, (1 + k)*k, (1 + k)*k^2, ..., (1+k)*k^(n-1), ...], with a(0) = 1, a(n) = (1+k)*k^(n-1) for n >= 1. Also a(n+1) = k*a(n) for n >= 1. - Zak Seidov and N. J. A. Sloane, Dec 05 2009
The g.f. (1+x)/(1-k*x) produces the sequence with closed form (in PARI notation) a(n)=(n>=0)*k^n+(n>=1)*k^(n-1). - Jaume Oliver Lafont, Dec 05 2009
Binomial transform of A000034. a(n) = (3*2^n - 0^n)/2. - Paul Barry, Apr 29 2003
a(n) = Sum_{k=0..n} (n+k)*binomial(n, k)/n. - Paul Barry, Jan 30 2005
a(n) = Sum_{k=0..n} A029653(n, k)*x^k for x = 1. - Philippe Deléham, Jul 10 2005
Binomial transform of A000034. Hankel transform is {1,-3,0,0,0,...}. - Paul Barry, Aug 29 2006
a(0) = 1, a(n) = 2 + Sum_{k=0..n-1} a(k) for n >= 1. - Joerg Arndt, Aug 15 2012
a(n) = 2^n + floor(2^(n-1)). - Martin Grymel, Oct 17 2012
E.g.f.: (3*exp(2*x) - 1)/2. - Stefano Spezia, Jan 31 2023

Edited by N. J. A. Sloane, Dec 04 2009

A167929 Number of reduced words of length n in Coxeter group on 19 generators S_i with relations (S_i)^2 = (S_i S_j)^16 = I.

Original entry on oeis.org

1, 19, 342, 6156, 110808, 1994544, 35901792, 646232256, 11632180608, 209379250944, 3768826516992, 67838877305856, 1221099791505408, 21979796247097344, 395636332447752192, 7121453984059539456

Offset: 0

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

nonn

The initial terms coincide with those of A170738, 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 (17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, -153).

Cf. A154638, A170738.

R:=PowerSeriesRing(Integers(), 20); Coefficients(R!( (1+x)*(1-x^16)/(1-18*x+170*x^16-153*x^17) )); // G. C. Greubel, Apr 26 2019

CoefficientList[Series[(1+x)*(1-x^16)/(1-18*x+170*x^16-153*x^17), {x, 0, 20}], x] (* G. C. Greubel, Jul 01 2016, modified Apr 26 2019 *)
coxG[{16, 153, -17}] (* The coxG program is at A169452 *) (* G. C. Greubel, Apr 26 2019 *)

my(x='x+O('x^20)); Vec((1+x)*(1-x^16)/(1-18*x+170*x^16-153*x^17)) \\ G. C. Greubel, Apr 26 2019

((1+x)*(1-x^16)/(1-18*x+170*x^16-153*x^17)).series(x, 20).coefficients(x, sparse=False) # G. C. Greubel, Apr 26 2019

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)/( 153*t^16 - 17*t^15 - 17*t^14 - 17*t^13 - 17*t^12 - 17*t^11 - 17*t^10 - 17*t^9 - 17*t^8 - 17*t^7 - 17*t^6 - 17*t^5 - 17*t^4 - 17*t^3 - 17*t^2 - 17*t + 1).
G.f.: (1+x)*(1-x^16)/(1 - 18*x + 170*x^16 - 153*x^17). - G. C. Greubel, Apr 26 2019
a(n) = -153*a(n-16) + 17*Sum_{k=1..15} a(n-k). - Wesley Ivan Hurt, May 06 2021

A167049 Number of reduced words of length n in Coxeter group on 19 generators S_i with relations (S_i)^2 = (S_i S_j)^13 = I.

Original entry on oeis.org

1, 19, 342, 6156, 110808, 1994544, 35901792, 646232256, 11632180608, 209379250944, 3768826516992, 67838877305856, 1221099791505408, 21979796247097173, 395636332447746036, 7121453984059373415

Offset: 0

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

nonn

The initial terms coincide with those of A170738, 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 (17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, -153).

R:=PowerSeriesRing(Integers(), 20); Coefficients(R!( (1+x)*(1-x^13)/(1-18*x+170*x^13-153*x^14) )); // G. C. Greubel, Apr 26 2019

CoefficientList[Series[(1+x)*(1-x^13)/(1-18*x+170*x^13-153*x^14), {x, 0, 20}], x] (* G. C. Greubel, May 31 2016, modified Apr 26 2019 *)
coxG[{13, 153, -17}] (* The coxG program is at A169452 *) (* G. C. Greubel, Apr 26 2019 *)

my(x='x+O('x^20)); Vec((1+x)*(1-x^13)/(1-18*x+170*x^13-153*x^14)) \\ G. C. Greubel, Apr 26 2019

((1+x)*(1-x^13)/(1-18*x+170*x^13-153*x^14)).series(x, 20).coefficients(x, sparse=False) # G. C. Greubel, Apr 26 2019

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)/(153*t^13 - 17*t^12 - 17*t^11 - 17*t^10 - 17*t^9 - 17*t^8 - 17*t^7 - 17*t^6 - 17*t^5 - 17*t^4 - 17*t^3 - 17*t^2 - 17*t + 1).
G.f.: (1+x)*(1-x^13)/(1 - 18*x + 170*x^13 - 153*x^14). - G. C. Greubel, Apr 26 2019
a(n) = -153*a(n-13) + 17*Sum_{k=1..12} a(n-k). - Wesley Ivan Hurt, May 06 2021

A163453 Number of reduced words of length n in Coxeter group on 19 generators S_i with relations (S_i)^2 = (S_i S_j)^5 = I.

Original entry on oeis.org

1, 19, 342, 6156, 110808, 1994373, 35895636, 646066215, 11628197676, 209289662676, 3766891838382, 67798255971825, 1220264268268608, 21962878883360919, 395298019772086050, 7114756005603413388

Offset: 0

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

The initial terms coincide with those of A170738, 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..790
Index entries for linear recurrences with constant coefficients, signature (17,17,17,17,-153).

R:=PowerSeriesRing(Integers(), 20); Coefficients(R!( (1+x)*(1-x^5)/(1-18*x+170*x^5-153*x^6) )); // G. C. Greubel, May 13 2019

CoefficientList[Series[(1+x)*(1-x^5)/(1-18*x+170*x^5-153*x^6), {x, 0, 20}], x] (* or *) LinearRecurrence[{17, 17, 17, 17, -153}, {1, 19, 342, 6156, 110808, 1994373}, 20] (* G. C. Greubel, Dec 24 2016 *)
coxG[{5, 153, -17}] (* The coxG program is at A169452 *) (* G. C. Greubel, May 13 2019 *)

my(x='x+O('x^20)); Vec((1+x)*(1-x^5)/(1-18*x+170*x^5-153*x^6)) \\ G. C. Greubel, Dec 24 2016

((1+x)*(1-x^5)/(1-18*x+170*x^5-153*x^6)).series(x, 20).coefficients(x, sparse=False) # G. C. Greubel, May 13 2019

G.f.: (t^5 + 2*t^4 + 2*t^3 + 2*t^2 + 2*t + 1)/(153*t^5 - 17*t^4 - 17*t^3 - 17*t^2 - 17*t + 1).

a(n) = 17*a(n-1)+17*a(n-2)+17*a(n-3)+17*a(n-4)-153*a(n-5). - Wesley Ivan Hurt, May 10 2021

A163968 Number of reduced words of length n in Coxeter group on 19 generators S_i with relations (S_i)^2 = (S_i S_j)^6 = I.

Original entry on oeis.org

1, 19, 342, 6156, 110808, 1994544, 35901621, 646226100, 11632014567, 209375268012, 3768736928724, 67836942598176, 1221059168656830, 21978960670333953, 395619413496128064, 7121115628832971863, 128179472668131616290, 2307219552362877498072, 41529754741525340825124

Offset: 0

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

The initial terms coincide with those of A170738, 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..795
Index entries for linear recurrences with constant coefficients, signature (17,17,17,17,17,-153).

a:=[19, 342, 6156, 110808, 1994544, 35901621];; for n in [7..30] do a[n]:=17*(a[n-1] +a[n-2]+a[n-3]+a[n-4]+a[n-5]) -153*a[n-6]; od; Concatenation([1], a); # G. C. Greubel, Aug 11 2019

R:=PowerSeriesRing(Integers(), 30); Coefficients(R!( (1+t)*(1-t^6)/(1-18*t+170*t^6-153*t^7) )); // G. C. Greubel, Aug 11 2019

seq(coeff(series((1+t)*(1-t^6)/(1-18*t+170*t^6-153*t^7), t, n+1), t, n), n = 0 .. 30); # G. C. Greubel, Aug 11 2019

CoefficientList[Series[(1+t)*(1-t^6)/(1-18*t+170*t^6-153*t^7), {t,0,30}], t] (* G. C. Greubel, Aug 23 2017 *)
coxG[{6, 153, -17}] (* The coxG program is at A169452 *) (* G. C. Greubel, Aug 11 2019 *)

my(t='t+O('t^30)); Vec((1+t)*(1-t^6)/(1-18*t+170*t^6-153*t^7)) \\ G. C. Greubel, Aug 23 2017

def A163968_list(prec):
    P. = PowerSeriesRing(ZZ, prec)
    return P((1+t)*(1-t^6)/(1-18*t+170*t^6-153*t^7)).list()
A163968_list(30) # G. C. Greubel, Aug 11 2019

G.f.: (t^6 + 2*t^5 + 2*t^4 + 2*t^3 + 2*t^2 + 2*t + 1)/(153*t^6 - 17*t^5 - 17*t^4 - 17*t^3 - 17*t^2 - 17*t + 1).

a(n) = -153*a(n-6) + 17*Sum_{k=1..5} a(n-k). - Wesley Ivan Hurt, May 11 2021

A165881 Number of reduced words of length n in Coxeter group on 19 generators S_i with relations (S_i)^2 = (S_i S_j)^10 = I.

Original entry on oeis.org

1, 19, 342, 6156, 110808, 1994544, 35901792, 646232256, 11632180608, 209379250944, 3768826516821, 67838877299700, 1221099791339367, 21979796243114412, 395636332358163924, 7121453982124831776

Offset: 0

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

nonn

The initial terms coincide with those of A170738, 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 (17,17,17,17,17,17,17,17,17,-153).

Cf. A154638, A170738.

a:=[19, 342, 6156, 110808, 1994544, 35901792, 646232256, 11632180608, 209379250944, 3768826516821];; for n in [11..20] do a[n]:=17*Sum([1..9], j-> a[n-j]) -153*a[n-10]; od; Concatenation([1], a); # G. C. Greubel, Sep 24 2019

R:=PowerSeriesRing(Integers(), 20); Coefficients(R!( (1+t)*(1-t^10)/(1-18*t+170*t^10-153*t^11) )); // G. C. Greubel, Sep 24 2019

seq(coeff(series((1+t)*(1-t^10)/(1-18*t+170*t^10-153*t^11), t, n+1), t, n), n = 0..20); # G. C. Greubel, Sep 24 2019

CoefficientList[Series[(1+t)*(1-t^10)/(1-18*t+170*t^10-153*t^11), {t, 0, 20}], t] (* G. C. Greubel, Apr 17 2016 *)
coxG[{10,153,-17}] (* The coxG program is at A169452 *) (* Harvey P. Dale, May 23 2017 *)

my(t='t+O('t^20)); Vec((1+t)*(1-t^10)/(1-18*t+170*t^10-153*t^11)) \\ G. C. Greubel, Sep 24 2019

def A163878_list(prec):
    P. = PowerSeriesRing(ZZ, prec)
    return P((1+t)*(1-t^10)/(1-18*t+170*t^10-153*t^11)).list()
A163878_list(20) # G. C. Greubel, Sep 24 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)/(153*t^10 - 17*t^9 - 17*t^8 - 17*t^7 - 17*t^6 - 17*t^5 - 17*t^4 - 17*t^3 - 17*t^2 - 17*t + 1).

A166413 Number of reduced words of length n in Coxeter group on 19 generators S_i with relations (S_i)^2 = (S_i S_j)^11 = I.

Original entry on oeis.org

1, 19, 342, 6156, 110808, 1994544, 35901792, 646232256, 11632180608, 209379250944, 3768826516992, 67838877305685, 1221099791499252, 21979796246931303, 395636332443769260, 7121453983969951188

Offset: 0

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

nonn

The initial terms coincide with those of A170738, 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 (17,17,17,17,17,17,17,17,17,17,-153).

Cf. A154638, A169452, A170738.

R:=PowerSeriesRing(Integers(), 30);
Coefficients(R!( (1+x)*(1-x^11)/(1-18*x+170*x^11-153*x^12) )); // G. C. Greubel, Jul 23 2024

With[{p=153, q=17}, CoefficientList[Series[(1+t)*(1-t^11)/(1-(q+1)*t + (p+q)*t^11-p*t^12), {t,0,40}], t]] (* G. C. Greubel, May 12 2016; Jul 23 2024 *)
coxG[{11,153,-17}] (* The coxG program is at A169452 *) (* Harvey P. Dale, Nov 26 2022 *)

def A166413_list(prec):
    P. = PowerSeriesRing(ZZ, prec)
    return P( (1+x)*(1-x^11)/(1-18*x+170*x^11-153*x^12) ).list()
A166413_list(30) # G. C. Greubel, Jul 23 2024

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)/(153*t^11 - 17*t^10 - 17*t^9 - 17*t^8 - 17*t^7 - 17*t^6 - 17*t^5 - 17*t^4 - 17*t^3 - 17*t^2 - 17*t + 1).
From G. C. Greubel, Jul 23 2024: (Start)
a(n) = 17*Sum_{j=1..10} a(n-j) - 153*a(n-11).
G.f.: (1+x)*(1-x^11)/(1 - 18*x + 170*x^11 - 153*x^12). (End)

A166600 Number of reduced words of length n in Coxeter group on 19 generators S_i with relations (S_i)^2 = (S_i S_j)^12 = I.

Original entry on oeis.org

1, 19, 342, 6156, 110808, 1994544, 35901792, 646232256, 11632180608, 209379250944, 3768826516992, 67838877305856, 1221099791505237, 21979796247091188, 395636332447586151, 7121453984055556524

Offset: 0

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

nonn

The initial terms coincide with those of A170738, 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 (17,17,17,17,17,17,17,17,17,17,17,-153).

Cf. A154638, A169452, A170738.

R:=PowerSeriesRing(Integers(), 40); Coefficients(R!( (1+x)*(1-x^12)/(1 - 18*x+170*x^12-153*x^13) )); // G. C. Greubel, Dec 08 2024

CoefficientList[Series[(1+t)*(1-t^12)/(1-18*t+170*t^12-153*t^13), {t, 0, 50}], t] (* G. C. Greubel, May 18 2016; Dec 08 2024 *)
coxG[{12,153,-17}] (* The coxG program is at A169452 *) (* Harvey P. Dale, Oct 05 2016 *)

def A166600_list(prec):
    P. = PowerSeriesRing(ZZ, prec)
    return P( (1+x)*(1-x^12)/(1-18*x+170*x^12-153*x^13) ).list()
print(A166600_list(40)) # G. C. Greubel, Dec 08 2024

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)/(153*t^12 - 17*t^11 - 17*t^10 - 17*t^9 -17*t^8 -17*t^7 - 17*t^6 - 17*t^5 - 17*t^4 - 17*t^3 - 17*t^2 -17*t + 1).
From G. C. Greubel, Dec 08 2024: (Start)
a(n) = 17*Sum_{j=1..11} a(n-j) - 153*a(n-12).
G.f.: (1+x)*(1-x^12)/(1 - 18*x + 170*x^12 - 153*x^13). (End)

A167126 Number of reduced words of length n in Coxeter group on 19 generators S_i with relations (S_i)^2 = (S_i S_j)^14 = I.

Original entry on oeis.org

1, 19, 342, 6156, 110808, 1994544, 35901792, 646232256, 11632180608, 209379250944, 3768826516992, 67838877305856, 1221099791505408, 21979796247097344, 395636332447752021, 7121453984059533300

Offset: 0

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

nonn

The initial terms coincide with those of A170738, 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 (17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, -153).

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)/ (153*t^14 - 17*t^13 - 17*t^12 - 17*t^11 - 17*t^10 - 17*t^9 - 17*t^8 - 17*t^7 - 17*t^6 - 17*t^5 - 17*t^4 - 17*t^3 - 17*t^2 - 17*t + 1), {t, 0, 50}], t] (* G. C. Greubel, Jun 04 2016 *)
coxG[{14,153,-17}] (* The coxG program is at A169452 *) (* Harvey P. Dale, Aug 03 2025 *)

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)/(153*t^14 - 17*t^13 - 17*t^12 - 17*t^11 - 17*t^10 - 17*t^9 - 17*t^8 - 17*t^7 - 17*t^6 - 17*t^5 - 17*t^4 - 17*t^3 - 17*t^2 - 17*t + 1).

A167676 Number of reduced words of length n in Coxeter group on 19 generators S_i with relations (S_i)^2 = (S_i S_j)^15 = I.

Original entry on oeis.org

1, 19, 342, 6156, 110808, 1994544, 35901792, 646232256, 11632180608, 209379250944, 3768826516992, 67838877305856, 1221099791505408, 21979796247097344, 395636332447752192, 7121453984059539285

Offset: 0

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

nonn

The initial terms coincide with those of A170738, 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 (17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, -153).

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)/(153*t^15 - 17*t^14 - 17*t^13 - 17*t^12 - 17*t^11 - 17*t^10 - 17*t^9 - 17*t^8 - 17*t^7 - 17*t^6 - 17*t^5 - 17*t^4 - 17*t^3 - 17*t^2 - 17*t + 1), {t, 0, 50}], t] (* G. C. Greubel, Jun 19 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)/(153*t^15 - 17*t^14 - 17*t^13 - 17*t^12 - 17*t^11 - 17*t^10 - 17*t^9 - 17*t^8 - 17*t^7 - 17*t^6 - 17*t^5 - 17*t^4 - 17*t^3 - 17*t^2 - 17*t + 1).

cp's OEIS Frontend

A003945 Expansion of g.f. (1+x)/(1-2*x).

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A167929 Number of reduced words of length n in Coxeter group on 19 generators S_i with relations (S_i)^2 = (S_i S_j)^16 = I.

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A167049 Number of reduced words of length n in Coxeter group on 19 generators S_i with relations (S_i)^2 = (S_i S_j)^13 = I.

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A163453 Number of reduced words of length n in Coxeter group on 19 generators S_i with relations (S_i)^2 = (S_i S_j)^5 = I.

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A163968 Number of reduced words of length n in Coxeter group on 19 generators S_i with relations (S_i)^2 = (S_i S_j)^6 = I.

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A165881 Number of reduced words of length n in Coxeter group on 19 generators S_i with relations (S_i)^2 = (S_i S_j)^10 = I.

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