A170762 -id:A170762 - 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

A218746 a(n) = (43^n - 1)/42.

Original entry on oeis.org

0, 1, 44, 1893, 81400, 3500201, 150508644, 6471871693, 278290482800, 11966490760401, 514559102697244, 22126041415981493, 951419780887204200, 40911050578149780601, 1759175174860440565844, 75644532518998944331293, 3252714898316954606245600, 139866740627629048068560801

Offset: 0

M. F. Hasler, Nov 04 2012

Partial sums of powers of 43 (A009987).

0 followed by the binomial transform of A170762. - R. J. Mathar, Jul 18 2015

Vincenzo Librandi, Table of n, a(n) for n = 0..600
Index entries related to partial sums
Index entries related to q-numbers
Index entries for linear recurrences with constant coefficients, signature (44,-43)

Cf. similar sequences of the form (k^n-1)/(k-1): A000225, A003462, A002450, A003463, A003464, A023000, A023001, A002452, A002275, A016123, A016125, A091030, A135519, A135518, A131865, A091045, A218721, A218722, A064108, A218724-A218734, A132469, A218736-A218753, A133853, A094028, A218723.

Cf. A009987, A170762.

[n le 2 select n-1 else 44*Self(n-1) - 43*Self(n-2): n in [1..20]]; // Vincenzo Librandi, Nov 07 2012

LinearRecurrence[{44, -43}, {0, 1}, 30] (* Vincenzo Librandi, Nov 07 2012 *)
Join[{0},Accumulate[43^Range[0,20]]] (* Harvey P. Dale, Jan 27 2015 *)

A218746(n):=(43^n-1)/42$
makelist(A218746(n),n,0,30); /* Martin Ettl, Nov 07 2012 */

PARI
```
A218746(n)=43^n\42
```

G.f.: x/((1-x)*(1-43*x)). - Vincenzo Librandi, Nov 07 2012
a(n) = 44*a(n-1) - 43*a(n-2). - Vincenzo Librandi, Nov 07 2012
a(n) = floor(43^n/42).  - Vincenzo Librandi, Nov 07 2012
E.g.f.: exp(22*x)*sinh(21*x)/21. - Elmo R. Oliveira, Aug 27 2024

A162881 Number of reduced words of length n in Coxeter group on 43 generators S_i with relations (S_i)^2 = (S_i S_j)^3 = I.

Original entry on oeis.org

1, 43, 1806, 74949, 3109932, 129025155, 5353007478, 222085686501, 9213895794684, 382266301290027, 15859472304395790, 657978118553895573, 27298209939779232636, 1132548704737573481379, 46987204341696557186262

Offset: 0

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

nonn

The initial terms coincide with those of A170762, 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 (41, 41, -861).

a:=[43,1806,74949];; for n in [4..20] do a[n]:=41*a[n-1]+41*a[n-2] -861*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)/(861*t^3-41*t^2-41*t+1))); // G. C. Greubel, Oct 24 2018

seq(coeff(series((x^3+2*x^2+2*x+1)/(861*x^3-41*x^2-41*x+1),x,n+1), x, n), n = 0 .. 20); # Muniru A Asiru, Oct 24 2018

CoefficientList[Series[(t^3+2*t^2+2*t+1)/(861*t^3-41*t^2-41*t+1), {t, 0, 20}], t] (* G. C. Greubel, Oct 24 2018 *)
coxG[{3, 861, -41}] (* The coxG program is at A169452 *) (* G. C. Greubel, Apr 27 2019 *)

my(t='t+O('t^20)); Vec((t^3+2*t^2+2*t+1)/(861*t^3-41*t^2-41*t+1)) \\ G. C. Greubel, Oct 24 2018

((1+x)*(1-x^3)/(1 -42*x +902*x^3 -861*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)/(861*t^3 - 41*t^2 - 41*t + 1).
a(n) = 41*a(n-1) + 41*a(n-2) - 861*a(n-3), n > 0. - Muniru A Asiru, Oct 24 2018
G.f.: (1+x)*(1-x^3)/(1 -42*x + 902*x^3 - 861*x^4). - G. C. Greubel, Apr 27 2019

A163226 Number of reduced words of length n in Coxeter group on 43 generators S_i with relations (S_i)^2 = (S_i S_j)^4 = I.

Original entry on oeis.org

1, 43, 1806, 75852, 3184881, 133727076, 5614945203, 235760834988, 9899147615406, 415646320207041, 17452195907135052, 732784406294332791, 30768219023291805678, 1291898809163525952060, 54244365975641552431917

Offset: 0

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

nonn

The initial terms coincide with those of A170762, 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..610
Index entries for linear recurrences with constant coefficients, signature (41, 41, 41, -861).

R:=PowerSeriesRing(Integers(), 20); Coefficients(R!( (1+x)*(1-x^4)/(1-42*x+902*x^4-861*x^5) )); // G. C. Greubel, Apr 30 2019

CoefficientList[Series[(t^4+2*t^3+2*t^2+2*t+1)/(861*t^4-41*t^3-41*t^2 - 41*t+1), {t,0,20}], t] (* or *) Join[{1}, LinearRecurrence[ {41, 41, 41, -861}, {43,1806,75852,3184881}, 20]] (* G. C. Greubel, Dec 11 2016 *)
coxG[{4, *61, -41}] (* 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)/(861*t^4-41*t^3 - 41*t^2-41*t+1)) \\ G. C. Greubel, Dec 11 2016

((1+x)*(1-x^4)/(1-42*x+902*x^4-861*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)/(861*t^4 - 41*t^3 - 41*t^2 - 41*t + 1).

a(n) = 41*a(n-1)+41*a(n-2)+41*a(n-3)-861*a(n-4). - Wesley Ivan Hurt, May 06 2021

A163745 Number of reduced words of length n in Coxeter group on 43 generators S_i with relations (S_i)^2 = (S_i S_j)^5 = I.

Original entry on oeis.org

1, 43, 1806, 75852, 3185784, 133802025, 5619647124, 236023587219, 9912923799660, 416339991317124, 17486161688852682, 734413837213650321, 30845173108213815708, 1295488532304021561975, 54410151353124129064362

Offset: 0

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

nonn

The initial terms coincide with those of A170762, 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..614
Index entries for linear recurrences with constant coefficients, signature (41, 41, 41, 41, -861).

R:=PowerSeriesRing(Integers(), 20); Coefficients(R!( (1+t)*(1-t^5)/(1-42*t+902*t^5-861*t^6) )); // G. C. Greubel, Aug 09 2019

seq(coeff(series((1+t)*(1-t^5)/(1-42*t+902*t^5-861*t^6), t, n+1), t, n), n = 0 .. 20); # G. C. Greubel, Aug 09 2019

CoefficientList[Series[(1+t)*(1-t^5)/(1-42*t+902*t^5-861*t^6), {t, 0, 20}], t] (* G. C. Greubel, Aug 02 2017 *)
coxG[{5, 865, -41}] (* The coxG program is at A169452 *) (* G. C. Greubel, Aug 09 2019 *)

my(t='t+O('t^20)); Vec((1+t)*(1-t^5)/(1-42*t+902*t^5-861*t^6)) \\ G. C. Greubel, Aug 02 2017

def A163745_list(prec):
    P. = PowerSeriesRing(ZZ, prec)
    return P((1+t)*(1-t^5)/(1-42*t+902*t^5-861*t^6)).list()
A163745_list(20) # G. C. Greubel, Aug 09 2019

G.f.: (t^5 + 2*t^4 + 2*t^3 + 2*t^2 + 2*t + 1)/(861*t^5 - 41*t^4 - 41*t^3 - 41*t^2 - 41*t + 1).

a(n) = 41*a(n-1)+41*a(n-2)+41*a(n-3)+41*a(n-4)-861*a(n-5). - Wesley Ivan Hurt, May 11 2021

A164113 Number of reduced words of length n in Coxeter group on 43 generators S_i with relations (S_i)^2 = (S_i S_j)^6 = I.

Original entry on oeis.org

1, 43, 1806, 75852, 3185784, 133802928, 5619722073, 236028289140, 9913186551891, 416353768315884, 17486855460998532, 734447811414657312, 30846803125630618266, 1295565523217549867745, 54413743236663181589148

Offset: 0

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

nonn

The initial terms coincide with those of A170762, 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..614
Index entries for linear recurrences with constant coefficients, signature (41,41,41,41,41,-861).

a:=[43, 1806, 75852, 3185784, 133802928, 5619722073];; for n in [7..30] do a[n]:=41*(a[n-1] +a[n-2]+a[n-3]+a[n-4]+a[n-5]) -861*a[n-6]; od; Concatenation([1], a); # G. C. Greubel, Aug 10 2019

R:=PowerSeriesRing(Integers(), 30); Coefficients(R!( (1+t)*(1-t^6)/(1-42*t+902*t^6-861*t^7) )); // G. C. Greubel, Aug 10 2019

seq(coeff(series((1+t)*(1-t^6)/(1-42*t+902*t^6-861*t^7), t, n+1), t, n), n = 0 .. 30); # G. C. Greubel, Aug 16 2019

CoefficientList[Series[(1+t)*(1-t^6)/(1-42*t+902*t^6-861*t^7), {t,0,30}], t] (* G. C. Greubel, Sep 11 2017 *)
coxG[{6, 861, -41}] (* The coxG program is at A169452 *) (* G. C. Greubel, Aug 16 2019 *)

my(t='t+O('t^30)); Vec((1+t)*(1-t^6)/(1-42*t+902*t^6-861*t^7)) \\ G. C. Greubel, Sep 11 2017

def A164113_list(prec):
    P. = PowerSeriesRing(ZZ, prec)
    return P((1+t)*(1-t^6)/(1-42*t+902*t^6-861*t^7)).list()
A164113_list(30) # G. C. Greubel, Aug 10 2019

G.f.: (t^6 + 2*t^5 + 2*t^4 + 2*t^3 + 2*t^2 + 2*t + 1)/(861*t^6 - 41*t^5 - 41*t^4 - 41*t^3 - 41*t^2 - 41*t + 1).

a(n) = -861*a(n-6) + 41*Sum_{k=1..5} a(n-k). - Wesley Ivan Hurt, May 11 2021

A166233 Number of reduced words of length n in Coxeter group on 43 generators S_i with relations (S_i)^2 = (S_i S_j)^10 = I.

Original entry on oeis.org

1, 43, 1806, 75852, 3185784, 133802928, 5619722976, 236028364992, 9913191329664, 416354035845888, 17486869505526393, 734448519232070580, 30846837807745372371, 1295567187925238776044, 54413821892857220325252

Offset: 0

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

nonn

The initial terms coincide with those of A170762, 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 (41, 41, 41, 41, 41, 41, 41, 41, 41, -861).

seq(coeff(series((1+t)*(1-t^10)/(1-42*t+902*t^10-861*t^11), t, n+1), t, n), n = 0 .. 30); # G. C. Greubel, Mar 11 2020

CoefficientList[Series[(1+t)*(1-t^10)/(1-42*t+902*t^10-861*t^11), {t,0,30}], t] (* G. C. Greubel, May 07 2016 *)
coxG[{10,861,-41}] (* The coxG program is at A169452 *) (* Harvey P. Dale, May 10 2018 *)

def A166233_list(prec):
    P. = PowerSeriesRing(ZZ, prec)
    return P( (1+t)*(1-t^10)/(1-42*t+902*t^10-861*t^11) ).list()
A166233_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)/(861*t^10 - 41*t^9 - 41*t^8 - 41*t^7 - 41*t^6 - 41*t^5 - 41*t^4 - 41*t^3 - 41*t^2 - 41*t + 1).

A166437 Number of reduced words of length n in Coxeter group on 43 generators S_i with relations (S_i)^2 = (S_i S_j)^11 = I.

Original entry on oeis.org

1, 43, 1806, 75852, 3185784, 133802928, 5619722976, 236028364992, 9913191329664, 416354035845888, 17486869505527296, 734448519232145529, 30846837807750074292, 1295567187925501528275, 54413821892870997324012

Offset: 0

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

nonn

The initial terms coincide with those of A170762, 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 (41,41,41,41,41,41,41,41,41,41,-861).

Cf. A154638, A169452, A170762.

R:=PowerSeriesRing(Integers(), 30);
f:= func< p,q,x | (1+x)*(1-x^11)/(1-(q+1)*x+(p+q)*x^11-p*x^12) >;
Coefficients(R!( f(861,41,x) )); // G. C. Greubel, Jul 26 2024

With[{p=861, q=41}, 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 14 2016; Jul 26 2024 *)
coxG[{11, 861, -41, 30}] (* The coxG program is at A169452 *) (* G. C. Greubel, Jul 26 2024 *)

def f(p,q,x): return (1+x)*(1-x^11)/(1-(q+1)*x+(p+q)*x^11-p*x^12)
def A166437_list(prec):
    P. = PowerSeriesRing(ZZ, prec)
    return P( f(861,41,x) ).list()
A166437_list(30) # G. C. Greubel, Jul 26 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)/(861*t^11 - 41*t^10 - 41*t^9 - 41*t^8 - 41*t^7 - 41*t^6 - 41*t^5 - 41*t^4 - 41*t^3 - 41*t^2 - 41*t + 1).
a(n) = -861*a(n-11) + 41*Sum_{k=1..10} a(n-k). - Wesley Ivan Hurt, Mar 17 2023
G.f.: (1+x)*(1-x^11)/(1 - 42*x + 902*x^11 - 861*x^12). - G. C. Greubel, Jul 26 2024

A166717 Number of reduced words of length n in Coxeter group on 43 generators S_i with relations (S_i)^2 = (S_i S_j)^12 = I.

Original entry on oeis.org

1, 43, 1806, 75852, 3185784, 133802928, 5619722976, 236028364992, 9913191329664, 416354035845888, 17486869505527296, 734448519232146432, 30846837807750149241, 1295567187925506230196, 54413821892871260076243

Offset: 0

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

nonn

The initial terms coincide with those of A170762, 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 (41, 41, 41, 41, 41, 41, 41, 41, 41, 41, 41, -861).

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)/(861*t^12 - 41*t^11 - 41*t^10 - 41*t^9 - 41*t^8 - 41*t^7 - 41*t^6 - 41*t^5 - 41*t^4 - 41*t^3 - 41*t^2 - 41*t + 1), {t, 0, 50}], t] (* G. C. Greubel, May 24 2016 *)

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)/(861*t^12 - 41*t^11 - 41*t^10 - 41*t^9 -41*t^8 -41*t^7 -41*t^6 - 41*t^5 - 41*t^4 - 41*t^3 - 41*t^2 - 41*t + 1).

A167096 Number of reduced words of length n in Coxeter group on 43 generators S_i with relations (S_i)^2 = (S_i S_j)^13 = I.

Original entry on oeis.org

1, 43, 1806, 75852, 3185784, 133802928, 5619722976, 236028364992, 9913191329664, 416354035845888, 17486869505527296, 734448519232146432, 30846837807750150144, 1295567187925506305145, 54413821892871264778164

Offset: 0

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

nonn

The initial terms coincide with those of A170762, 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 (41, 41, 41, 41, 41, 41, 41, 41, 41, 41, 41, 41, -861).

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)/(861*t^13 - 41*t^12 - 41*t^11 - 41*t^10 - 41*t^9 - 41*t^8 - 41*t^7 - 41*t^6 - 41*t^5 - 41*t^4 - 41*t^3 - 41*t^2 - 41*t + 1), {t, 0, 50}], t] (* G. C. Greubel, Jun 02 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)/(861*t^13 - 41*t^12 - 41*t^11 - 41*t^10 - 41*t^9 - 41*t^8 - 41*t^7 - 41*t^6 - 41*t^5 - 41*t^4 - 41*t^3 - 41*t^2 - 41*t + 1).

cp's OEIS Frontend

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

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A218746 a(n) = (43^n - 1)/42.

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A162881 Number of reduced words of length n in Coxeter group on 43 generators S_i with relations (S_i)^2 = (S_i S_j)^3 = I.

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A163226 Number of reduced words of length n in Coxeter group on 43 generators S_i with relations (S_i)^2 = (S_i S_j)^4 = I.

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A163745 Number of reduced words of length n in Coxeter group on 43 generators S_i with relations (S_i)^2 = (S_i S_j)^5 = I.

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A164113 Number of reduced words of length n in Coxeter group on 43 generators S_i with relations (S_i)^2 = (S_i S_j)^6 = I.

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