A154638 -id:A154638 - cp's OEIS frontend

A163217 Number of reduced words of length n in Coxeter group on 34 generators S_i with relations (S_i)^2 = (S_i S_j)^4 = I.

1, 34, 1122, 37026, 1221297, 40284288, 1328771136, 43829305344, 1445702699760, 47686274735616, 1572924224543232, 51882656590093824, 1711341215834452224, 56448319139710451712, 1861938872397761101824, 61415759005426222645248

Offset: 0

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

The initial terms coincide with those of A170753, 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..650
Index entries for linear recurrences with constant coefficients, signature (32, 32, 32, -528).

Cf. A154638, A170753.

a:=[34,1122,37026,1221297];; for n in [5..20] do a[n]:=32*(a[n-1]+ a[n-2]+a[n-3]) -528*a[n-4]; od; Concatenation([1], a); # G. C. Greubel, Apr 28 2019

R:=PowerSeriesRing(Integers(), 20); Coefficients(R!( (1+x)*(1-x^4)/(1-33*x+560*x^4-528*x^5) )); // G. C. Greubel, Apr 28 2019

CoefficientList[Series[(t^4+2*t^3+2*t^2+2*t+1)/(528*t^4-32*t^3-32*t^2 - 32*t+1), {t,0,20}], t] (* or *)
LinearRecurrence[{32, 32, 32, -528}, {1, 34, 1122, 37026, 1221297}, 20] (* G. C. Greubel, Dec 11 2016; simplified by Georg Fischer, Apr 08 2019 *)
coxG[{4,528,-32}] (* The coxG program is at A169452 *) (* Harvey P. Dale, Jul 06 2018 *)

my(x='x+O('x^20)); Vec((1+x)*(1-x^4)/(1-33*x+560*x^4-528*x^5)) \\ G. C. Greubel, Dec 11 2016, modified Apr 28 2019

((1+x)*(1-x^4)/(1-33*x+560*x^4-528*x^5)).series(x, 20).coefficients(x, sparse=False) # G. C. Greubel, Apr 28 2019

G.f.: (t^4 + 2*t^3 + 2*t^2 + 2*t + 1)/(528*t^4 - 32*t^3 - 32*t^2 - 32*t + 1).
From G. C. Greubel, Apr 28 2019: (Start)
a(n) = 32*(a(n-1) + a(n-2) + a(n-3)) - 528*a(n-4).
G.f.: (1+x)*(1-x^4)/(1 - 33*x + 560*x^4 - 528*x^5). (End)

A163218 Number of reduced words of length n in Coxeter group on 35 generators S_i with relations (S_i)^2 = (S_i S_j)^4 = I.

Original entry on oeis.org

1, 35, 1190, 40460, 1375045, 46731300, 1588176975, 53974651500, 1834344072330, 62340711467265, 2118667029023160, 72003509011079415, 2447059985777227590, 83164038200838759780, 2826353783752411211145, 96054447135432681999180

Offset: 0

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

nonn

The initial terms coincide with those of A170754, 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..650
Index entries for linear recurrences with constant coefficients, signature (33, 33, 33, -561).

R:=PowerSeriesRing(Integers(), 20); Coefficients(R!( (1+x)*(1-x^4)/(1-34*x+594*x^4-x^561*x^5) )); // G. C. Greubel, Apr 30 2019

CoefficientList[Series[(t^4+2*t^3+2*t^2+2*t+1)/(561*t^4-33*t^3-33*t^2 - 33*t+1), {t,0,20}], t] (* or *) LinearRecurrence[{33, 33, 33, -561}, {1, 35, 1190, 40460}, 20] (* G. C. Greubel, Dec 11 2016 *)
coxG[{4, 561, -33}] (* 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)/(561*t^4-33*t^3 - 33*t^2-33*t+1)) \\ G. C. Greubel, Dec 11 2016

((1+x)*(1-x^4)/(1-34*x+594*x^4-561*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)/(561*t^4 - 33*t^3 - 33*t^2 - 33*t + 1).

a(n) = -561*a(n-4) + 33*Sum_{k=1..3} a(n-k). - Wesley Ivan Hurt, May 05 2021

A163219 Number of reduced words of length n in Coxeter group on 36 generators S_i with relations (S_i)^2 = (S_i S_j)^4 = I.

Original entry on oeis.org

1, 36, 1260, 44100, 1542870, 53978400, 1888472880, 66069561600, 2311490430270, 80869130653500, 2829263840578980, 98983800307381500, 3463018394666864670, 121156152466965222600, 4238733846520797445080, 148295107229819712107400

Offset: 0

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

The initial terms coincide with those of A170755, 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..645
Index entries for linear recurrences with constant coefficients, signature (34, 34, 34, -595).

Cf. A154638, A170755.

R:=PowerSeriesRing(Integers(), 20); Coefficients(R!( (1+x)*(1-x^4)/(1-35*x+629*x^4-595*x^5) )); // G. C. Greubel, Apr 30 2019

CoefficientList[Series[(t^4+2*t^3+2*t^2+2*t+1)/(595*t^4-34*t^3-34*t^2 - 34*t+1), {t, 0, 20}], t] (* or *) Join[{1}, LinearRecurrence[{34, 34, 34, -595}, {36, 1260, 44100, 1542870}, 20]] (* G. C. Greubel, Dec 11 2016 *)
coxG[{4, 595, -34}] (* 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)/(595*t^4-34*t^3 - 34*t^2-34*t+1)) \\ G. C. Greubel, Dec 11 2016

((1+x)*(1-x^4)/(1-35*x+629*x^4-595*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)/(595*t^4 - 34*t^3 - 34*t^2 - 34*t + 1).

a(n) = -595*a(n-4) + 34*Sum_{k=1..3} a(n-k). - Wesley Ivan Hurt, May 05 2021

A163220 Number of reduced words of length n in Coxeter group on 37 generators S_i with relations (S_i)^2 = (S_i S_j)^4 = I.

Original entry on oeis.org

1, 37, 1332, 47952, 1725606, 62097840, 2234659770, 80416702800, 2893883982570, 104139615440700, 3747579228757350, 134860782963557700, 4853114416362432150, 174644689291688511000, 6284782282271390399250

Offset: 0

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

nonn

The initial terms coincide with those of A170756, 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..640
Index entries for linear recurrences with constant coefficients, signature (35, 35, 35, -630).

R:=PowerSeriesRing(Integers(), 20); Coefficients(R!( (1+x)*(1-x^4)/(1-36*x+665*x^4-630*x^5) )); // G. C. Greubel, Apr 30 2019

CoefficientList[Series[(t^4+2*t^3+2*t^2+2*t+1)/(630*t^4-35*t^3-35*t^2 - 35*t+1), {t,0,20}], t] (* or *) LinearRecurrence[{35, 35, 35, -630}, {1, 37, 1332, 47952}, 20] (* G. C. Greubel, Dec 11 2016 *)
coxG[{4, 630, -35}] (* 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)/(630*t^4-35*t^3 - 35*t^2-35*t+1)) \\ G. C. Greubel, Dec 11 2016

((1+x)*(1-x^4)/(1-36*x+665*x^4-630*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)/(630*t^4 - 35*t^3 - 35*t^2 - 35*t + 1).

a(n) = -630*a(n-4) + 35*Sum_{k=1..3} a(n-k). - Wesley Ivan Hurt, May 05 2021

A163221 Number of reduced words of length n in Coxeter group on 38 generators S_i with relations (S_i)^2 = (S_i S_j)^4 = I.

Original entry on oeis.org

1, 38, 1406, 52022, 1924111, 71166096, 2632183848, 97355219328, 3600827035866, 133181923185576, 4925930761424952, 182192847843197736, 6738672428195210748, 249239784283952410080, 9218502714272560450272

Offset: 0

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

nonn

The initial terms coincide with those of A170757, 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..635
Index entries for linear recurrences with constant coefficients, signature (36, 36, 36, -666).

a:=[38,1406,52022,1924111];; for n in [5..20] do a[n]:=36*(a[n-1]+ a[n-2]+a[n-3]) -666*a[n-4]; od; Concatenation([1], a); # G. C. Greubel, May 01 2019

R:=PowerSeriesRing(Integers(), 20); Coefficients(R!( (1+x)*(1-x^4)/(1-37*x+702*x^4-666*x^5) )); // G. C. Greubel, May 01 2019

coxG[{4,666,-36}] (* The coxG program is at A169452 *) (* Harvey P. Dale, Jul 09 2015 *)
CoefficientList[Series[(t^4+2*t^3+2*t^2+2*t+1)/(666*t^4-36*t^3-36*t^2 - 36*t+1), {t,0,20}], t] (* or *) LinearRecurrence[{36, 36, 36, -666}, {1, 38, 1406, 52022, 1924111}, 20] (* G. C. Greubel, Dec 11 2016; modified by Georg Fischer, Apr 08 2019 *)

my(t='t+O('t^20)); Vec((t^4+2*t^3+2*t^2+2*t+1)/(666*t^4-36*t^3 - 36*t^2-36*t+1)) \\ G. C. Greubel, Dec 11 2016

((1+x)*(1-x^4)/(1-37*x+702*x^4-666*x^5)).series(x, 20).coefficients(x, sparse=False) # G. C. Greubel, May 01 2019

G.f.: (t^4 + 2*t^3 + 2*t^2 + 2*t + 1)/(666*t^4 - 36*t^3 - 36*t^2 - 36*t + 1).

a(n) = 36*a(n-1)+36*a(n-2)+36*a(n-3)-666*a(n-4). - Wesley Ivan Hurt, May 06 2021

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

A163223 Number of reduced words of length n in Coxeter group on 40 generators S_i with relations (S_i)^2 = (S_i S_j)^4 = I.

Original entry on oeis.org

1, 40, 1560, 60840, 2371980, 92476800, 3605409600, 140564736000, 5480222014020, 213658376756760, 8329936604744040, 324760699264187160, 12661502336823753660, 493636212105145265520, 19245481572342746507280

Offset: 0

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

nonn

The initial terms coincide with those of A170759, 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..625
Index entries for linear recurrences with constant coefficients, signature (38, 38, 38, -741).

Cf. A154638, A170759.

R:=PowerSeriesRing(Integers(), 20); Coefficients(R!( (1+x)*(1-x^4)/(1-39*x+779*x^4-741*x^5) )); // G. C. Greubel, Apr 30 2019

CoefficientList[Series[(t^4+2*t^3+2*t^2+2*t+1)/(741*t^4-38*t^3-38*t^2 - 38*t+1), {t, 0, 20}], t] (* or *) LinearRecurrence[{38, 38, 38, -741}, {1, 40, 1560, 60840, 2371980}, 20] (* G. C. Greubel, Dec 11 2016 *)
coxG[{4, 741, -38}] (* 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)/(741*t^4- 38*t^3 -38*t^2-38*t+1)) \\ G. C. Greubel, Dec 11 2016

((1+x)*(1-x^4)/(1-39*x+779*x^4-741*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)/(741*t^4 - 38*t^3 - 38*t^2 - 38*t + 1).

a(n) = 38*a(n-1)+38*a(n-2)+38*a(n-3)-741*a(n-4). - Wesley Ivan Hurt, May 06 2021

A163224 Number of reduced words of length n in Coxeter group on 41 generators S_i with relations (S_i)^2 = (S_i S_j)^4 = I.

Original entry on oeis.org

1, 41, 1640, 65600, 2623180, 104894400, 4194464820, 167726145600, 6706948607580, 268194081870000, 10724409825744420, 428842296999090000, 17148329715447559980, 685718769084764781600, 27420176663127165184020

Offset: 0

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

nonn

The initial terms coincide with those of A170760, 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..620
Index entries for linear recurrences with constant coefficients, signature (39,39,39,-780).

R:=PowerSeriesRing(Integers(), 20); Coefficients(R!( (1+x)*(1-x^4)/(1-40*x+819*x^4-780*x^5) )); // G. C. Greubel, Apr 30 2019

CoefficientList[Series[(t^4+2*t^3+2*t^2+2*t+1)/(780*t^4-39*t^3-39*t^2 - 39*t+1), {t,0,20}], t] (* or *) Join[{1}, LinearRecurrence[ {39, 39, 39, -780}, {41,1640,65600,2623180} 20]] (* G. C. Greubel, Dec 11 2016 *)
coxG[{4,780,-39}] (* The coxG program is at A169452 *) (* Harvey P. Dale, Jan 18 2019 *)

my(t='t+O('t^20)); Vec((t^4+2*t^3+2*t^2+2*t+1)/(780*t^4-39*t^3- 39*t^2-39*t+1)) \\ G. C. Greubel, Dec 11 2016

((1+x)*(1-x^4)/(1-40*x+819*x^4-780*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)/(780*t^4 - 39*t^3 - 39*t^2 - 39*t + 1).

a(n) = 39*a(n-1)+39*a(n-2)+39*a(n-3)-780*a(n-4). - Wesley Ivan Hurt, May 06 2021

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

A163230 Number of reduced words of length n in Coxeter group on 44 generators S_i with relations (S_i)^2 = (S_i S_j)^4 = I.

Original entry on oeis.org

1, 44, 1892, 81356, 3497362, 150345888, 6463124976, 277839201024, 11943854101410, 513446807614356, 22072240836651852, 948849634132915284, 40789498214388049434, 1753474001285744132472, 75378987430163637459624

Offset: 0

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

nonn

The initial terms coincide with those of A170763, 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..600
Index entries for linear recurrences with constant coefficients, signature (42, 42, 42, -903).

R:=PowerSeriesRing(Integers(), 20); Coefficients(R!( (1+x)*(1-x^4)/(1-43*x+945*x^4-903*x^5) )); // G. C. Greubel, Apr 30 2019

coxG[{4,903,-42}] (* The coxG program is at A169452 *) (* Harvey P. Dale, Apr 18 2015 *)
CoefficientList[Series[(t^4+2*t^3+2*t^2+2*t+1)/(903*t^4-42*t^3-42*t^2 - 42*t+1), {t,0,20}], t] (* or *) Join[{1}, LinearRecurrence[ {42, 42, 42, -903}, {44,1892,81356,3497362}, 50]] (* G. C. Greubel, Dec 11 2016 *)

my(t='t+O('t^20)); Vec((t^4+2*t^3+2*t^2+2*t+1)/(903*t^4-42*t^3 - 42*t^2-42*t+1)) \\ G. C. Greubel, Dec 11 2016

((1+x)*(1-x^4)/(1-43*x+945*x^4-903*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)/(903*t^4 - 42*t^3 - 42*t^2 - 42*t + 1).

a(n) = 42*a(n-1)+42*a(n-2)+42*a(n-3)-903*a(n-4). - Wesley Ivan Hurt, May 06 2021

cp's OEIS Frontend

A163217 Number of reduced words of length n in Coxeter group on 34 generators S_i with relations (S_i)^2 = (S_i S_j)^4 = I.

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A163218 Number of reduced words of length n in Coxeter group on 35 generators S_i with relations (S_i)^2 = (S_i S_j)^4 = I.

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A163219 Number of reduced words of length n in Coxeter group on 36 generators S_i with relations (S_i)^2 = (S_i S_j)^4 = I.

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A163220 Number of reduced words of length n in Coxeter group on 37 generators S_i with relations (S_i)^2 = (S_i S_j)^4 = I.

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A163221 Number of reduced words of length n in Coxeter group on 38 generators S_i with relations (S_i)^2 = (S_i S_j)^4 = I.

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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.

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A163223 Number of reduced words of length n in Coxeter group on 40 generators S_i with relations (S_i)^2 = (S_i S_j)^4 = I.

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