A170747 -id:A170747 - 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

A164664 Number of reduced words of length n in Coxeter group on 28 generators S_i with relations (S_i)^2 = (S_i S_j)^7 = I.

Original entry on oeis.org

1, 28, 756, 20412, 551124, 14880348, 401769396, 10847773314, 292889869272, 7908026195160, 213516699839352, 5764950695053368, 155653663349994264, 4202648764205784984, 113471512684966713186, 3063730735882188973692

Offset: 0

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

nonn

The initial terms coincide with those of A170747, 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..695
Index entries for linear recurrences with constant coefficients, signature (26,26,26,26,26,26,-351).

Cf. A154638, A170747.

a:=[28,756,20412,551124,14880348,401769396,10847773314];; for n in [8..30] do a[n]:=26*(a[n-1] +a[n-2]+a[n-3]+a[n-4]+a[n-5]+a[n-6]) -351*a[n-7]; od; Concatenation([1], a); # G. C. Greubel, Sep 15 2019

R:=PowerSeriesRing(Integers(), 20); Coefficients(R!( (1+t)*(1-t^7)/(1-27*t+377*t^7-351*t^8) )); // G. C. Greubel, Sep 15 2019

seq(coeff(series((1+t)*(1-t^7)/(1-27*t+377*t^7-351*t^8), t, n+1), t, n), n = 0 .. 30); # G. C. Greubel, Sep 15 2019

CoefficientList[Series[(t^7 + 2*t^6 + 2*t^5 + 2*t^4 + 2*t^3 + 2*t^2 + 2*t + 1)/(351*t^7 - 26*t^6 - 26*t^5 - 26*t^4 - 26*t^3 - 26*t^2 - 26*t + 1), {t, 0, 20}], t] (* Wesley Ivan Hurt, Apr 25 2017 *)
coxG[{7,351,-26}] (* The coxG program is at A169452 *) (* Harvey P. Dale, Aug 13 2018 *)

my(t='t+O('t^20)); Vec((1+t)*(1-t^7)/(1-27*t+377*t^7-351*t^8)) \\ G. C. Greubel, Sep 15 2019

def A164664_list(prec):
    P. = PowerSeriesRing(ZZ, prec)
    return P((1+t)*(1-t^7)/(1-27*t+377*t^7-351*t^8)).list()
A164664_list(20) # G. C. Greubel, Sep 15 2019

G.f.: (t^7 + 2*t^6 + 2*t^5 + 2*t^4 + 2*t^3 + 2*t^2 + 2*t + 1)/(351*t^7 - 26*t^6 - 26*t^5 - 26*t^4 - 26*t^3 - 26*t^2 - 26*t + 1).

A163548 Number of reduced words of length n in Coxeter group on 28 generators S_i with relations (S_i)^2 = (S_i S_j)^5 = I.

Original entry on oeis.org

1, 28, 756, 20412, 551124, 14879970, 401748984, 10846947384, 292860149400, 7907023424664, 213484216161762, 5763927599870076, 155622096911221668, 4201690015605193020, 113442752267421552612, 3062876603036110993314

Offset: 0

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

nonn

The initial terms coincide with those of A170747, 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..695
Index entries for linear recurrences with constant coefficients, signature (26, 26, 26, 26, -351).

R:=PowerSeriesRing(Integers(), 20); Coefficients(R!( (1+x)*(1-x^5)/(1-27*x+377*x^5-351*x^6) )); // G. C. Greubel, May 16 2019

CoefficientList[Series[(1+x)*(1-x^5)/(1-27*x+377*x^5-351*x^6), {x, 0, 20}], x] (* G. C. Greubel, Jul 27 2017 *)
coxG[{5,351,-26}] (* The coxG program is at A169452 *) (* Harvey P. Dale, Apr 05 2018 *)

my(x='x+O('x^20)); Vec((1+x)*(1-x^5)/(1-27*x+377*x^5-351*x^6)) \\ G. C. Greubel, Jul 27 2017

((1+x)*(1-x^5)/(1-27*x+377*x^5-351*x^6)).series(x, 20).coefficients(x, sparse=False) # G. C. Greubel, May 16 2019

G.f.: (t^5 + 2*t^4 + 2*t^3 + 2*t^2 + 2*t + 1)/(351*t^5 - 26*t^4 - 26*t^3 - 26*t^2 - 26*t + 1).

a(n) = 26*a(n-1)+26*a(n-2)+26*a(n-3)+26*a(n-4)-351*a(n-5). - Wesley Ivan Hurt, May 10 2021

A164025 Number of reduced words of length n in Coxeter group on 28 generators S_i with relations (S_i)^2 = (S_i S_j)^6 = I.

Original entry on oeis.org

1, 28, 756, 20412, 551124, 14880348, 401769018, 10847753280, 292889063376, 7907997281184, 213515725982832, 5764919185089792, 155652671753506746, 4202618188762620900, 113470584484975272828, 3063702902583418604964

Offset: 0

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

nonn

The initial terms coincide with those of A170747, 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..695
Index entries for linear recurrences with constant coefficients, signature (26,26,26,26,26,-351).

a:=[28, 756, 20412, 551124, 14880348, 401769018];; for n in [7..30] do a[n]:=26*(a[n-1] +a[n-2]+a[n-3]+a[n-4]+a[n-5]) -351*a[n-6]; od; Concatenation([1], a); # G. C. Greubel, Aug 13 2019

R:=PowerSeriesRing(Integers(), 30); Coefficients(R!( (1+t)*(1-t^6)/(1-27*t+377*t^6-351*t^7) )); // G. C. Greubel, Aug 13 2019

seq(coeff(series((1+t)*(1-t^6)/(1-27*t+377*t^6-351*t^7), t, n+1), t, n), n = 0 .. 30); # G. C. Greubel, Aug 13 2019

CoefficientList[Series[(1+t)*(1-t^6)/(1-27*t+377*t^6-351*t^7), {t,0,30}], t] (* G. C. Greubel, Sep 07 2017 *)
coxG[{6, 351, -26}] (* The coxG program is at A169452 *) (* G. C. Greubel, Aug 10 2019 *)

my(t='t+O('t^30)); Vec((1+t)*(1-t^6)/(1-27*t+377*t^6-351*t^7)) \\ G. C. Greubel, Sep 07 2017

def A164025_list(prec):
    P. = PowerSeriesRing(ZZ, prec)
    return P((1+t)*(1-t^6)/(1-27*t+377*t^6-351*t^7)).list()
A164025_list(30) # G. C. Greubel, Aug 13 2019

G.f.: (t^6 + 2*t^5 + 2*t^4 + 2*t^3 + 2*t^2 + 2*t + 1)/(351*t^6 - 26*t^5 - 26*t^4 - 26*t^3 - 26*t^2 - 26*t + 1).

a(n) = -351*a(n-6) + 26*Sum_{k=1..5} a(n-k). - Wesley Ivan Hurt, May 11 2021

A165456 Number of reduced words of length n in Coxeter group on 28 generators S_i with relations (S_i)^2 = (S_i S_j)^9 = I.

Original entry on oeis.org

1, 28, 756, 20412, 551124, 14880348, 401769396, 10847773692, 292889889684, 7908027021090, 213516729559224, 5764951697823864, 155653695833814360, 4202649787312378584, 113471544252017775096, 3063731694658235867448

Offset: 0

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

The initial terms coincide with those of A170747, 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..695
Index entries for linear recurrences with constant coefficients, signature (26,26,26,26,26,26,26,26,-351).

a:=[28, 756, 20412, 551124, 14880348, 401769396, 10847773692, 292889889684, 7908027021090];; for n in [10..20] do a[n]:=326*Sum([1..8], j-> a[n-j]) -351*a[n-9]; od; Concatenation([1], a); # G. C. Greubel, Sep 16 2019

R:=PowerSeriesRing(Integers(), 20); Coefficients(R!( (1+t)*(1-t^9)/(1-27*t+377*t^9-351*t^10) )); // G. C. Greubel, Oct 20 2018

seq(coeff(series((x^9+2*x^8+2*x^7+2*x^6+2*x^5+2*x^4+2*x^3+2*x^2+2*x+1)/( 351*x^9-26*x^8-26*x^7-26*x^6-26*x^5-26*x^4-26*x^3-26*x^2-26*x+1),x, n+1), x, n), n = 0 .. 15); # Muniru A Asiru, Oct 21 2018

CoefficientList[Series[(1+t)*(1-t^9)/(1-27*t+377*t^9-351*t^10), {t, 0, 30}], t] (* G. C. Greubel, Oct 20 2018 *)
coxG[{9, 351, -26}] (* The coxG program is at A169452 *) (* G. C. Greubel, Sep 16 2019 *)

my(t='t+O('t^20)); Vec((1+t)*(1-t^9)/(1-27*t+377*t^9-351*t^10)) \\ G. C. Greubel, Oct 20 2018

def A165456_list(prec):
    P. = PowerSeriesRing(ZZ, prec)
    return P((1+t)*(1-t^9)/(1-27*t+377*t^9-351*t^10)).list()
A165456_list(20) # G. C. Greubel, Sep 16 2019

G.f.: (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)/(351*t^9 - 26*t^8 - 26*t^7 - 26*t^6 - 26*t^5 - 26*t^4 - 26*t^3 -26*t^2 - 26*t + 1).

A165980 Number of reduced words of length n in Coxeter group on 28 generators S_i with relations (S_i)^2 = (S_i S_j)^10 = I.

Original entry on oeis.org

1, 28, 756, 20412, 551124, 14880348, 401769396, 10847773692, 292889889684, 7908027021468, 213516729579258, 5764951698629760, 155653695862728336, 4202649788286235104, 113471544283527738672, 3063731695649832497472

Offset: 0

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

nonn

The initial terms coincide with those of A170747, 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 (26,26,26,26,26,26,26,26,26,-351).

a:=[28, 756, 20412, 551124, 14880348, 401769396, 10847773692, 292889889684, 7908027021468, 213516729579258];; for n in [11..30] do a[n]:=26*Sum([1..9], j-> a[n-j]) - 351*a[n-10]; od; Concatenation([1], a); # G. C. Greubel, Oct 25 2019

R:=PowerSeriesRing(Integers(), 30); Coefficients(R!( (1+t)*(1-t^10)/(1-27*t+377*t^10-351*t^11) )); // G. C. Greubel, Oct 25 2019

seq(coeff(series((1+t)*(1-t^10)/(1-27*t+377*t^10-351*t^11), t, n+1), t, n), n = 0..30); # G. C. Greubel, Oct 25 2019

CoefficientList[Series[(1+t)*(1-t^10)/(1-27*t+377*t^10-351*t^11), {t, 0, 30}], t] (* G. C. Greubel, Apr 20 2016 *)
coxG[{10, 351, -26}] (* The coxG program is at A169452 *) (* G. C. Greubel, Oct 25 2019 *)

my(t='t+O('t^30)); Vec((1+t)*(1-t^10)/(1-27*t+377*t^10-351*t^11)) \\ G. C. Greubel, Oct 25 2019

def A165980_list(prec):
    P. = PowerSeriesRing(ZZ, prec)
    return P((1+t)*(1-t^10)/(1-27*t+377*t^10-351*t^11)).list()
A165980_list(30) # G. C. Greubel, Oct 25 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)/(351*t^10 - 26*t^9 - 26*t^8 - 26*t^7 - 26*t^6 - 26*t^5 - 26*t^4 - 26*t^3 - 26*t^2 - 26*t + 1).

A166422 Number of reduced words of length n in Coxeter group on 28 generators S_i with relations (S_i)^2 = (S_i S_j)^11 = I.

Original entry on oeis.org

1, 28, 756, 20412, 551124, 14880348, 401769396, 10847773692, 292889889684, 7908027021468, 213516729579636, 5764951698649794, 155653695863534232, 4202649788315149080, 113471544284501595192, 3063731695681342461048

Offset: 0

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

nonn

The initial terms coincide with those of A170747, 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 (26,26,26,26,26,26,26,26,26,26,-351).

Cf. A154638, A169452, A170747.

R:=PowerSeriesRing(Integers(), 30);
Coefficients(R!( (1+x)*(1-x^11)/(1-27*x+377*x^11-351*x^12) )); // G. C. Greubel, Jul 25 2024

With[{p=351, q=26}, 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 13 2016; Jul 25 2024 *)
coxG[{11,351,-26}] (* The coxG program is at A169452 *) (* Harvey P. Dale, Dec 22 2019 *)

def A166422_list(prec):
    P. = PowerSeriesRing(ZZ, prec)
    return P( (1+x)*(1-x^11)/(1-27*x+377*x^11-351*x^12) ).list()
A166422_list(30) # G. C. Greubel, Jul 25 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)/(351*t^11 - 26*t^10 - 26*t^9 - 26*t^8 - 26*t^7 - 26*t^6 - 26*t^5 - 26*t^4 - 26*t^3 - 26*t^2 - 26*t + 1).
From G. C. Greubel, Jul 25 2024: (Start)
a(n) = 26*Sum_{j=1..10} a(n-j) - 351*a(n-11).
G.f.: (1+x)*(1-x^11)/(1 - 27*x + 377*x^11 - 351*x^12). (End)

A166615 Number of reduced words of length n in Coxeter group on 28 generators S_i with relations (S_i)^2 = (S_i S_j)^12 = I.

Original entry on oeis.org

1, 28, 756, 20412, 551124, 14880348, 401769396, 10847773692, 292889889684, 7908027021468, 213516729579636, 5764951698650172, 155653695863554266, 4202649788315954976, 113471544284530509168, 3063731695682316317568

Offset: 0

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

nonn

The initial terms coincide with those of A170747, 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 (26, 26, 26, 26, 26, 26, 26, 26, 26, 26, 26, -351).

CoefficientList[Series[(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)/(351*t^12 - 26*t^11 - 26*t^10 - 26*t^9 - 26*t^8 - 26*t^7 - 26*t^6 - 26*t^5 - 26*t^4 - 26*t^3 - 26*t^2 - 26*t + 1), {t, 0, 50}], t](* G. C. Greubel, May 19 2016 *)
coxG[{12,351,-26}] (* The coxG program is at A169452 *) (* Harvey P. Dale, Jun 22 2020 *)

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)/(351*t^12 - 26*t^11 - 26*t^10 - 26*t^9 -26*t^8 -26*t^7 - 26*t^6 - 26*t^5 - 26*t^4 - 26*t^3 - 26*t^2 - 26*t +1).

A167081 Number of reduced words of length n in Coxeter group on 28 generators S_i with relations (S_i)^2 = (S_i S_j)^13 = I.

Original entry on oeis.org

1, 28, 756, 20412, 551124, 14880348, 401769396, 10847773692, 292889889684, 7908027021468, 213516729579636, 5764951698650172, 155653695863554644, 4202649788315975010, 113471544284531315064, 3063731695682345231544

Offset: 0

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

nonn

The initial terms coincide with those of A170747, 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 (26, 26, 26, 26, 26, 26, 26, 26, 26, 26, 26, 26, -351).

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)/(351*t^13 - 26*t^12 - 26*t^11 - 26*t^10 - 26*t^9 - 26*t^8 - 26*t^7 - 26*t^6 - 26*t^5 - 26*t^4 - 26*t^3 - 26*t^2 - 26*t + 1), {t, 0, 50}], t] (* G. C. Greubel, May 31 2016 *)
coxG[{13,351,-26}] (* The coxG program is at A169452 *) (* Harvey P. Dale, Oct 16 2016 *)

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)/(351*t^13 - 26*t^12 - 26*t^11 - 26*t^10 - 26*t^9 - 26*t^8 - 26*t^7 - 26*t^6 - 26*t^5 - 26*t^4 - 26*t^3 - 26*t^2 - 26*t + 1).

A167235 Number of reduced words of length n in Coxeter group on 28 generators S_i with relations (S_i)^2 = (S_i S_j)^14 = I.

Original entry on oeis.org

1, 28, 756, 20412, 551124, 14880348, 401769396, 10847773692, 292889889684, 7908027021468, 213516729579636, 5764951698650172, 155653695863554644, 4202649788315975388, 113471544284531335098, 3063731695682346037440

Offset: 0

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

nonn

The initial terms coincide with those of A170747, 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 (26, 26, 26, 26, 26, 26, 26, 26, 26, 26, 26, 26, 26, -351).

coxG[{14,351,-26}] (* The coxG program is at A169452 *) (* Harvey P. Dale, Jun 05 2016 *)
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)/ (351*t^14 - 26*t^13 - 26*t^12 - 26*t^11 - 26*t^10 - 26*t^9 - 26*t^8 - 26*t^7 - 26*t^6 - 26*t^5 - 26*t^4 - 26*t^3 - 26*t^2 - 26*t + 1), {t, 0, 50}], t] (* G. C. Greubel, Jun 05 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)/(351*t^14 - 26*t^13 - 26*t^12 - 26*t^11 - 26*t^10 - 26*t^9 - 26*t^8 - 26*t^7 - 26*t^6 - 26*t^5 - 26*t^4 - 26*t^3 - 26*t^2 - 26*t + 1).

cp's OEIS Frontend

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

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A164664 Number of reduced words of length n in Coxeter group on 28 generators S_i with relations (S_i)^2 = (S_i S_j)^7 = I.

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A163548 Number of reduced words of length n in Coxeter group on 28 generators S_i with relations (S_i)^2 = (S_i S_j)^5 = I.

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A164025 Number of reduced words of length n in Coxeter group on 28 generators S_i with relations (S_i)^2 = (S_i S_j)^6 = I.

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A165456 Number of reduced words of length n in Coxeter group on 28 generators S_i with relations (S_i)^2 = (S_i S_j)^9 = I.

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A165980 Number of reduced words of length n in Coxeter group on 28 generators S_i with relations (S_i)^2 = (S_i S_j)^10 = I.

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