A170758 -id:A170758 - 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

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)

A164681 Number of reduced words of length n in Coxeter group on 39 generators S_i with relations (S_i)^2 = (S_i S_j)^7 = I.

Original entry on oeis.org

1, 39, 1482, 56316, 2140008, 81320304, 3090171552, 117426518235, 4462207664772, 169563890192073, 6443427786666780, 244850254349321868, 9304309606601631648, 353563762821303227856, 13435422902486289765684

Offset: 0

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

The initial terms coincide with those of A170758, 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..200
Index entries for linear recurrences with constant coefficients, signature (37, 37, 37, 37, 37, 37, -703).

R:=PowerSeriesRing(Integers(), 20); Coefficients(R!( (1+x)*(1-x^7)/(1 -38*x +740*x^7 -703*x^8) )); // G. C. Greubel, Apr 26 2019

CoefficientList[Series[(x^7 + 2 x^6 + 2 x^5 + 2 x^4 + 2 x^3 + 2 x^2 + 2 x + 1)/(703 x^7 - 37 x^6 - 37 x^5 - 37 x^4 - 37 x^3 - 37 x^2 - 37 x + 1), {x, 0, 20}], x ] (* Vincenzo Librandi, Apr 29 2014 *)
coxG[{7, 703, -37}] (* The coxG program is at A169452 *) (* G. C. Greubel, Apr 26 2019 *)

my(x='x+O('x^20)); Vec((1+x)*(1-x^7)/(1-38*x+740*x^7-703*x^8)) \\ G. C. Greubel, Apr 26 2019

((1+x)*(1-x^7)/(1 -38*x +740*x^7 -703*x^8)).series(x, 20).coefficients(x, sparse=False) # G. C. Greubel, Apr 26 2019

G.f.: (x^7 + 2*x^6 + 2*x^5 + 2*x^4 + 2*x^3 + 2*x^2 + 2*x + 1)/(703*x^7 - 37*x^6 - 37*x^5 - 37*x^4 - 37*x^3 - 37*x^2 - 37*x + 1).

G.f.: (1+x)*(1-x^7)/(1 -38*x +740*x^7 -703*x^8). - G. C. Greubel, Apr 26 2019

A166691 Number of reduced words of length n in Coxeter group on 39 generators S_i with relations (S_i)^2 = (S_i S_j)^12 = I.

Original entry on oeis.org

1, 39, 1482, 56316, 2140008, 81320304, 3090171552, 117426518976, 4462207721088, 169563893401344, 6443427949251072, 244850262071540736, 9304309958718547227, 353563778431304766468, 13435423580389580056521

Offset: 0

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

nonn

The initial terms coincide with those of A170758, 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 (37, 37, 37, 37, 37, 37, 37, 37, 37, 37, 37, -703).

R:=PowerSeriesRing(Integers(), 20); Coefficients(R!( (1+x)*(1-x^12)/(1-38*x+740*x^12-703*x^13) )); // G. C. Greubel, Apr 26 2019

CoefficientList[Series[(1+x)*(1-x^12)/(1-38*x+740*x^12-703*x^13), {x, 0, 20}], x] (* G. C. Greubel, May 23 2016, modified Apr 26 2019 *)
coxG[{12,703,-37}] (* The coxG program is at A169452 *) (* Harvey P. Dale, Jan 10 2017 *)

my(x='x+O('x^20)); Vec((1+x)*(1-x^12)/(1-38*x+740*x^12-703*x^13)) \\ G. C. Greubel, Apr 26 2019

((1+x)*(1-x^12)/(1-38*x+740*x^12-703*x^13)).series(x, 20).coefficients(x, sparse=False) # G. C. Greubel, Apr 26 2019

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)/(703*t^12 - 37*t^11 - 37*t^10 - 37*t^9 -37*t^8 -37*t^7 -37*t^6 - 37*t^5 - 37*t^4 - 37*t^3 - 37*t^2 - 37*t + 1).
G.f.: (1+x)*(1-x^12)/(1 -38*x +740*x^12 -703*x^13). - G. C. Greubel, Apr 26 2019
a(n) = -703*a(n-12) + 37*Sum_{k=1..11} a(n-k). - Wesley Ivan Hurt, May 06 2021

A167942 Number of reduced words of length n in Coxeter group on 27 generators S_i with relations (S_i)^2 = (S_i S_j)^16 = I.

Original entry on oeis.org

1, 27, 702, 18252, 474552, 12338352, 320797152, 8340725952, 216858874752, 5638330743552, 146596599332352, 3811511582641152, 99099301148669952, 2576581829865418752, 66991127576500887552, 1741769316989023076352

Offset: 0

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

nonn

The initial terms coincide with those of A170746, 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 (25,25,25,25,25,25,25,25,25,25,25,25,25,25,25,-325).

Cf. A154638, A169452, A170758.

R:=PowerSeriesRing(Integers(), 40); Coefficients(R!( (1+x)*(1-x^16)/(1-26*x+350*x^16-325*x^17) )); // G. C. Greubel, Sep 08 2023

CoefficientList[Series[(1+t)*(1-t^16)/(1-26*t+350*t^16-325*t^17), {t, 0, 50}], t] (* G. C. Greubel, Jul 01 2016; Sep 08 2023 *)
coxG[{16,325,-25}] (* The coxG program is at A169452 *) (* Harvey P. Dale, Oct 28 2018 *)

def A167942_list(prec):
    P. = PowerSeriesRing(ZZ, prec)
    return P( (1+x)*(1-x^16)/(1-26*x+350*x^16-325*x^17) ).list()
A167942_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)/( 325*t^16 - 25*t^15 - 25*t^14 - 25*t^13 - 25*t^12 - 25*t^11 - 25*t^10 - 25*t^9 - 25*t^8 - 25*t^7 - 25*t^6 - 25*t^5 - 25*t^4 - 25*t^3 - 25*t^2 - 25*t + 1).
From G. C. Greubel, Sep 08 2023: (Start)
G.f.: (1+t)*(1-t^16)/(1 - 26*t + 350*t^16 - 325*t^17).
a(n) = 25*Sum_{j=1..15} a(n-j) - 325*a(n-16). (End)

A162871 Number of reduced words of length n in Coxeter group on 39 generators S_i with relations (S_i)^2 = (S_i S_j)^3 = I.

Original entry on oeis.org

1, 39, 1482, 55575, 2083692, 78111033, 2928135600, 109766289945, 4114781688966, 154249795892907, 5782323668697966, 216760526662519203, 8125647855742321632, 304604136609884440797, 11418619374984439210164

Offset: 0

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

nonn

The initial terms coincide with those of A170758, 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..615
Index entries for linear recurrences with constant coefficients, signature (37, 37, -703).

a:=[39,1482,55575];; for n in [4..15] do a[n]:=37*a[n-1]+37*a[n-2]-703*a[n-3]; od; Concatenation([1],a); # Muniru A Asiru, Oct 24 2018

R:=PowerSeriesRing(Integers(), 20); Coefficients(R!((t^3 + 2*t^2+2*t+1)/(703*t^3-37*t^2-37*t+1))); // G. C. Greubel, Oct 24 2018

seq(coeff(series((x^3+2*x^2+2*x+1)/(703*x^3-37*x^2-37*x+1),x,n+1), x, n), n = 0 .. 20); # Muniru A Asiru, Oct 24 2018

coxG[{3,703,-37}] (* The coxG program is at A169452 *) (* Harvey P. Dale, Jun 25 2018 *)
CoefficientList[Series[(t^3+2*t^2+2*t+1)/(703*t^3-37*t^2-37*t+1), {t, 0, 20}], t] (* G. C. Greubel, Oct 24 2018 *)

my(t='t+O('t^20)); Vec((t^3+2*t^2+2*t+1)/(703*t^3-37*t^2-37*t+1)) \\ G. C. Greubel, Oct 24 2018

((1+x)*(1-x^3)/(1 -38*x +740*x^3 -703*x^4)).series(x, 20).coefficients(x, sparse=False) # G. C. Greubel, Apr 27 2019

G.f.: (t^3 + 2*t^2 + 2*t + 1)/(703*t^3 - 37*t^2 - 37*t + 1).
a(n) = 37*a(n-1) + 37*a(n-2) - 703*a(n-3), n > 0. - Muniru A Asiru, Oct 24 2018
G.f.: (1+x)*(1-x^3)/(1 - 38*x + 740*x^3 - 703*x^4). - G. C. Greubel, Apr 27 2019

A163222 Number of reduced words of length n in Coxeter group on 39 generators S_i with relations (S_i)^2 = (S_i S_j)^4 = I.

Original entry on oeis.org

1, 39, 1482, 56316, 2139267, 81263988, 3086962281, 117263934684, 4454486050560, 169211838474861, 6427822638540342, 244172655087350379, 9275347010187982854, 352341101130365494992, 13384324210123816783899

Offset: 0

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

nonn

The initial terms coincide with those of A170758, 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..630
Index entries for linear recurrences with constant coefficients, signature (37, 37, 37, -703).

R:=PowerSeriesRing(Integers(), 20); Coefficients(R!( (1+x)*(1-x^4)/(1-38*x+740*x^4-703*x^5) )); // G. C. Greubel, Apr 30 2019

CoefficientList[Series[(t^4+2*t^3+2*t^2+2*t+1)/(703*t^4-37*t^3-37*t^2 - 37*t+1), {t,0,20}], t] (* or *) Join[{1}, LinearRecurrence[{37, 37, 37, -703}, {39, 1482, 56316, 2139267}, 20]] (* G. C. Greubel, Dec 11 2016 *)
coxG[{4, 703, -37}] (* The coxG program is at A169452 *) (* G. C. Greubel, Apr 30 2019 *)

my(t='t+O('t^20)); Vec((t^4+2*t^3+2*t^2+2*t+1)/(703*t^4-37*t^3 - 37*t^2-37*t+1)) \\ G. c. Greubel, Dec 11 2016

((1+x)*(1-x^4)/(1-38*x+740*x^4-703*x^5)).series(x, 20).coefficients(x, sparse=False) # G. C. Greubel, Apr 30 2019

G.f.: (t^4 + 2*t^3 + 2*t^2 + 2*t + 1)/(703*t^4 - 37*t^3 - 37*t^2 - 37*t + 1).

a(n) = 37*a(n-1)+37*a(n-2)+37*a(n-3)-703*a(n-4). - Wesley Ivan Hurt, May 06 2021

A163668 Number of reduced words of length n in Coxeter group on 39 generators S_i with relations (S_i)^2 = (S_i S_j)^5 = I.

Original entry on oeis.org

1, 39, 1482, 56316, 2140008, 81319563, 3090115236, 117423309705, 4462045136796, 169556171182476, 6443075832883092, 244834652131935645, 9303632060115383718, 353534798919570074859, 13434200024194718979990

Offset: 0

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

nonn

The initial terms coincide with those of A170758, 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..630
Index entries for linear recurrences with constant coefficients, signature (37, 37, 37, 37, -703).

a:=[39, 1482, 56316, 2140008, 81319563];; for n in [6..20] do a[n]:=37*(a[n-1]+a[n-2] +a[n-3]+a[n-4]) -703*a[n-5]; od; Concatenation([1], a); # G. C. Greubel, May 23 2019

R:=PowerSeriesRing(Integers(), 20); Coefficients(R!( (1+x)*(1-x^5)/(1-38*x+740*x^5-703*x^6) )); // G. C. Greubel, May 23 2019

CoefficientList[Series[(1+x)*(1-x^5)/(1-38*x+740*x^5-703*x^6), {x, 0, 20}], x] (* G. C. Greubel, Aug 01 2017 *)
coxG[{5, 703, -37}] (* The coxG program is at A169452 *) (* G. C. Greubel, May 23 2019 *)

my(x='x+O('x^20)); Vec((1+x)*(1-x^5)/(1-38*x+740*x^5-703*x^6)) \\ G. C. Greubel, Aug 01 2017

((1+x)*(1-x^5)/(1-38*x+740*x^5-703*x^6)).series(x, 20).coefficients(x, sparse=False) # G. C. Greubel, May 23 2019

G.f.: (t^5 + 2*t^4 + 2*t^3 + 2*t^2 + 2*t + 1)/(703*t^5 - 37*t^4 - 37*t^3 - 37*t^2 - 37*t + 1).

a(n) = 37*a(n-1)+37*a(n-2)+37*a(n-3)+37*a(n-4)-703*a(n-5). - Wesley Ivan Hurt, May 11 2021

A166171 Number of reduced words of length n in Coxeter group on 39 generators S_i with relations (S_i)^2 = (S_i S_j)^10 = I.

Original entry on oeis.org

1, 39, 1482, 56316, 2140008, 81320304, 3090171552, 117426518976, 4462207721088, 169563893401344, 6443427949250331, 244850262071484420, 9304309958715338697, 353563778431142238492, 13435423580381861046924

Offset: 0

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

nonn

The initial terms coincide with those of A170758, 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 (37, 37, 37, 37, 37, 37, 37, 37, 37, -703).

seq(coeff(series((1+t)*(1-t^10)/(1-38*t+740*t^10-703*t^11), t, n+1), t, n), n = 0 .. 30); # G. C. Greubel, Mar 11 2020

CoefficientList[Series[(1+t)*(1-t^10)/(1-38*t+740*t^10-703*t^11), {t,0,30}], t] (* G. C. Greubel, May 06 2016 *)
coxG[{703, 10, -37}] (* The coxG program is in A169452 *) (* G. C. Greubel, Mar 11 2020 *)

def A166171_list(prec):
    P. = PowerSeriesRing(ZZ, prec)
    return P( (1+t)*(1-t^10)/(1-38*t+740*t^10-703*t^11) ).list()
A166171_list(30) # G. C. Greubel, Aug 10 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)/(703*t^10 - 37*t^9 - 37*t^8 - 37*t^7 - 37*t^6 - 37*t^5 - 37*t^4 - 37*t^3 - 37*t^2 - 37*t + 1).

cp's OEIS Frontend

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

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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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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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A164681 Number of reduced words of length n in Coxeter group on 39 generators S_i with relations (S_i)^2 = (S_i S_j)^7 = I.

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A166691 Number of reduced words of length n in Coxeter group on 39 generators S_i with relations (S_i)^2 = (S_i S_j)^12 = I.

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A167942 Number of reduced words of length n in Coxeter group on 27 generators S_i with relations (S_i)^2 = (S_i S_j)^16 = I.

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A162871 Number of reduced words of length n in Coxeter group on 39 generators S_i with relations (S_i)^2 = (S_i S_j)^3 = I.

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