A169452 -id:A169452 - cp's OEIS frontend

A163440 Number of reduced words of length n in Coxeter group on 15 generators S_i with relations (S_i)^2 = (S_i S_j)^5 = I.

1, 15, 210, 2940, 41160, 576135, 8064420, 112881405, 1580053020, 22116729180, 309578036040, 4333306233165, 60655281460410, 849019887139515, 11884122064943310, 166347525415813560, 2328442863574420320

Offset: 0

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

nonn

The initial terms coincide with those of A170734, 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..855
Index entries for linear recurrences with constant coefficients, signature (13, 13, 13, 13, -91).

R:=PowerSeriesRing(Integers(), 30); Coefficients(R!( (1+x)*(1-x^5)/(1-14*x+104*x^5-91*x^6) )); // G. C. Greubel, May 12 2019

CoefficientList[Series[(1+x)*(1-x^5)/(1-14*x+104*x^5-91*x^6), {x, 0, 30}], x] (* or *) LinearRecurrence[{13, 13, 13, 13, -91}, {15, 210, 2940, 41160, 576135}, 30] (* G. C. Greubel, Dec 23 2016 *)
coxG[{5, 91, -13}] (* The coxG program is at A169452 *) (* G. C. Greubel, May 12 2019 *)

my(x='x+O('x^30)); Vec((1+x)*(1-x^5)/(1-14*x+104*x^5-91*x^6)) \\ G. C. Greubel, Dec 23 2016

((1+x)*(1-x^5)/(1-14*x+104*x^5-91*x^6)).series(x, 30).coefficients(x, sparse=False) # G. C. Greubel, May 12 2019

G.f.: (t^5 + 2*t^4 + 2*t^3 + 2*t^2 + 2*t + 1)/(91*t^5 - 13*t^4 - 13*t^3 - 13*t^2 - 13*t + 1).

a(n) = 13*a(n-1)+13*a(n-2)+13*a(n-3)+13*a(n-4)-91*a(n-5). - Wesley Ivan Hurt, May 10 2021

A163441 Number of reduced words of length n in Coxeter group on 16 generators S_i with relations (S_i)^2 = (S_i S_j)^5 = I.

Original entry on oeis.org

1, 16, 240, 3600, 54000, 809880, 12146400, 182169120, 2732133600, 40975956000, 614548634280, 9216869130000, 138232634196720, 2073183516810000, 31093163487414000, 466328623499110680, 6993897072666789600

Offset: 0

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

nonn

The initial terms coincide with those of A170735, 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..845
Index entries for linear recurrences with constant coefficients, signature (14, 14, 14, 14, -105).

R:=PowerSeriesRing(Integers(), 20); Coefficients(R!( (1+x)*(1-x^5)/(1-15*x+119*x^5-105*x^6) )); // G. C. Greubel, May 13 2019

CoefficientList[Series[(1+x)*(1-x^5)/(1-15*x+119*x^5-105*x^6), {x, 0, 20}], x] (* or *) LinearRecurrence[{14, 14, 14, 14, -105}, {1, 16, 240, 3600, 54000, 809880}, 20] (* G. C. Greubel, Dec 23 2016 *)
coxG[{5, 105, -14}] (* The coxG program is at A169452 *) (* G. C. Greubel, May 13 2019 *)

my(x='x+O('x^20)); Vec((1+x)*(1-x^5)/(1-15*x+119*x^5-105*x^6)) \\ G. C. Greubel, Dec 23 2016

((1+x)*(1-x^5)/(1-15*x+119*x^5-105*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)/(105*t^5 - 14*t^4 - 14*t^3 - 14*t^2 - 14*t + 1).

a(n) = 14*a(n-1)+14*a(n-2)+14*a(n-3)+14*a(n-4)-105*a(n-5). - Wesley Ivan Hurt, May 10 2021

A163451 Number of reduced words of length n in Coxeter group on 17 generators S_i with relations (S_i)^2 = (S_i S_j)^5 = I.

Original entry on oeis.org

1, 17, 272, 4352, 69632, 1113976, 17821440, 285108360, 4561178880, 72969984000, 1167377713080, 18675771192000, 298775988016200, 4779834262113600, 76468044587443200, 1223339873805905400, 19571056837109136000

Offset: 0

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

nonn

The initial terms coincide with those of A170736, 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..825
Index entries for linear recurrences with constant coefficients, signature (15, 15, 15, 15, -120).

R:=PowerSeriesRing(Integers(), 20); Coefficients(R!( (1+x)*(1-x^5)/(1-16*x+135*x^5-120*x^6) )); // G. C. Greubel, May 13 2019

CoefficientList[Series[(1+x)*(1-x^5)/(1-16*x+135*x^5-120*x^6), {x, 0, 20}], x] (* G. C. Greubel, Dec 24 2016 *)
coxG[{5, 120, -15}] (* The coxG program is at A169452 *) (* G. C. Greubel, May 13 2019 *)

my(x='x+O('x^20)); Vec((1+x)*(1-x^5)/(1-16*x+135*x^5-120*x^6)) \\ G. C. Greubel, Dec 24 2016

((1+x)*(1-x^5)/(1-16*x+135*x^5-120*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)/(120*t^5 - 15*t^4 - 15*t^3 - 15*t^2 - 15*t + 1).

a(n) = 15*a(n-1)+15*a(n-2)+15*a(n-3)+15*a(n-4)-120*a(n-5). - Wesley Ivan Hurt, May 10 2021

A163452 Number of reduced words of length n in Coxeter group on 18 generators S_i with relations (S_i)^2 = (S_i S_j)^5 = I.

Original entry on oeis.org

1, 18, 306, 5202, 88434, 1503225, 25552224, 434343744, 7383094560, 125499873024, 2133281378232, 36262103930496, 616393221671808, 10477621608796800, 178101495469706112, 3027418232198243904, 51460888233840150528

Offset: 0

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

nonn

The initial terms coincide with those of A170737, 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..800
Index entries for linear recurrences with constant coefficients, signature (16, 16, 16, 16, -136).

R:=PowerSeriesRing(Integers(), 20); Coefficients(R!( (1+x)*(1-x^5)/(1-17*x+152*x^5-136*x^6) )); // G. C. Greubel, May 13 2019

CoefficientList[Series[(1+x)*(1-x^5)/(1-17*x+152*x^5-136*x^6), {x, 0, 20}], x] (* or *)  LinearRecurrence[{16,16,16,16,-136}, {1, 18, 306, 5202, 88434, 1503225}, 20] (* G. C. Greubel, Dec 24 2016 *)
coxG[{5, 136, -16}] (* The coxG program is at A169452 *) (* G. C. Greubel, May 13 2019 *)

my(x='x+O('x^20)); Vec((1+x)*(1-x^5)/(1-17*x+152*x^5-136*x^6)) \\ G. C. Greubel, Dec 24 2016

((1+x)*(1-x^5)/(1-17*x+152*x^5-136*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)/(136*t^5 - 16*t^4 - 16*t^3 - 16*t^2 - 16*t + 1).

a(n) = 16*a(n-1)+16*a(n-2)+16*a(n-3)+16*a(n-4)-136*a(n-5). - Wesley Ivan Hurt, May 10 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

A163454 Number of reduced words of length n in Coxeter group on 20 generators S_i with relations (S_i)^2 = (S_i S_j)^5 = I.

Original entry on oeis.org

1, 20, 380, 7220, 137180, 2606230, 49514760, 940712040, 17872229160, 339547661640, 6450936451470, 122558879953620, 2328449391567180, 44237321450224020, 840447989197392780, 15967350630411275430

Offset: 0

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

nonn

The initial terms coincide with those of A170739, 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..750
Index entries for linear recurrences with constant coefficients, signature (18, 18, 18, 18, -171).

R:=PowerSeriesRing(Integers(), 20); Coefficients(R!( (1+x)*(1-x^5)/(1-19*x+189*x^5-171*x^6) )); // G. C. Greubel, May 13 2019

CoefficientList[Series[(1+x)*(1-x^5)/(1-19*x+189*x^5-171*x^6), {x, 0, 20}], x] (* or *) LinearRecurrence[{18, 18, 18, 18, -171}, {1, 20, 380, 7220, 137180, 2606230}, 20] (* G. C. Greubel, Dec 24 2016 *)
coxG[{5, 171, -18}] (* The coxG program is at A169452 *) (* G. C. Greubel, May 13 2019 *)

my(x='x+O('x^20)); Vec((1+x)*(1-x^5)/(1-19*x+189*x^5-171*x^6)) \\ G. C. Greubel, Dec 24 2016

((1+x)*(1-x^5)/(1-19*x+189*x^5-171*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)/(171*t^5 - 18*t^4 - 18*t^3 - 18*t^2 - 18*t + 1).

a(n) = 18*a(n-1)+18*a(n-2)+18*a(n-3)+18*a(n-4)-171*a(n-5). - Wesley Ivan Hurt, May 10 2021

A163503 Number of reduced words of length n in Coxeter group on 21 generators S_i with relations (S_i)^2 = (S_i S_j)^5 = I.

Original entry on oeis.org

1, 21, 420, 8400, 168000, 3359790, 67191600, 1343748210, 26873288400, 537432252000, 10747974763890, 214946090593500, 4298653734898110, 85967713492846500, 1719247052441058000, 34382796834223386990

Offset: 0

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

nonn

The initial terms coincide with those of A170740, 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..765
Index entries for linear recurrences with constant coefficients, signature (19, 19, 19, 19, -190).

R:=PowerSeriesRing(Integers(), 20); Coefficients(R!( (1+x)*(1-x^5)/(1-20*x+209*x^5-190*x^6) )); // G. C. Greubel, May 16 2019

coxG[{5,190,-19}] (* The coxG program is at A169452 *) (* Harvey P. Dale, Jul 09 2015 *)
CoefficientList[Series[(1+x)*(1-x^5)/(1-20*x+209*x^5-190*x^6), {x,0,20}], x] (* G. C. Greubel, Jul 26 2017 *)

my(x='x+O('x^20)); Vec((1+x)*(1-x^5)/(1-20*x+209*x^5-190*x^6)) \\ G. C. Greubel, Jul 26 2017

((1+x)*(1-x^5)/(1-20*x+209*x^5-190*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)/(190*t^5 - 19*t^4 - 19*t^3 - 19*t^2 - 19*t + 1).

a(n) = 19*a(n-1)+19*a(n-2)+19*a(n-3)+19*a(n-4)-190*a(n-5). - Wesley Ivan Hurt, May 10 2021

A163514 Number of reduced words of length n in Coxeter group on 22 generators S_i with relations (S_i)^2 = (S_i S_j)^5 = I.

Original entry on oeis.org

1, 22, 462, 9702, 203742, 4278351, 89840520, 1886549280, 39615400440, 831878586000, 17468509071090, 366818925627000, 7702782398341800, 161749714998425400, 3396561002126245800, 71323937982067871100

Offset: 0

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

The initial terms coincide with those of A170741, 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..750
Index entries for linear recurrences with constant coefficients, signature (20, 20, 20, 20, -210).

R:=PowerSeriesRing(Integers(), 20); Coefficients(R!( (1+x)*(1-x^5)/(1-21*x+230*x^5-210*x^6) )); // G. C. Greubel, May 16 2019

CoefficientList[Series[(1+x)*(1-x^5)/(1-21*x+230*x^5-210*x^6), {x, 0, 20}], x] (* G. C. Greubel, Jul 27 2017 *)
coxG[{5, 210, -20}] (* The coxG program is at A169452 *) (* G. C. Greubel, May 16 2019 *)

my(x='x+O('x^20)); Vec((1+x)*(1-x^5)/(1-21*x+230*x^5-210*x^6)) \\ G. C. Greubel, Jul 27 2017

((1+x)*(1-x^5)/(1-21*x+230*x^5-210*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)/(210*t^5 - 20*t^4 - 20*t^3 - 20*t^2 - 20*t + 1).

a(n) = -210*a(n-5) + 20*Sum_{k=1..4} a(n-k). - Wesley Ivan Hurt, May 05 2021

A163518 Number of reduced words of length n in Coxeter group on 23 generators S_i with relations (S_i)^2 = (S_i S_j)^5 = I.

Original entry on oeis.org

1, 23, 506, 11132, 244904, 5387635, 118522404, 2607370689, 57359466780, 1261849124844, 27759379635372, 610677728876061, 13434280356535038, 295540315560771435, 6501582206394337062, 143028104664155140584

Offset: 0

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

The initial terms coincide with those of A170742, 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..740
Index entries for linear recurrences with constant coefficients, signature (21, 21, 21, 21, -231).

R:=PowerSeriesRing(Integers(), 20); Coefficients(R!( (1+x)*(1-x^5)/(1-22*x+252*x^5-231*x^6) )); // G. C. Greubel, May 16 2019

CoefficientList[Series[(1+x)*(1-x^5)/(1-22*x+252*x^5-231*x^6), {x, 0, 20}], x] (* G. C. Greubel, Jul 27 2017 *)
coxG[{5, 231, -21}] (* The coxG program is at A169452 *) (* G. C. Greubel, May 16 2019 *)

my(x='x+O('x^20)); Vec((1+x)*(1-x^5)/(1-22*x+252*x^5-231*x^6)) \\ G. C. Greubel, Jul 27 2017

((1+x)*(1-x^5)/(1-22*x+252*x^5-231*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)/(231*t^5 - 21*t^4 - 21*t^3 - 21*t^2 - 21*t + 1).

a(n) = 21*a(n-1)+21*a(n-2)+21*a(n-3)+21*a(n-4)-231*a(n-5). - Wesley Ivan Hurt, May 10 2021

A163519 Number of reduced words of length n in Coxeter group on 24 generators S_i with relations (S_i)^2 = (S_i S_j)^5 = I.

Original entry on oeis.org

1, 24, 552, 12696, 292008, 6715908, 154459536, 3552423600, 81702391056, 1879077904176, 43217018799372, 993950655137880, 22859927229943848, 525756756894338904, 12091909332851083560, 278102505382114851108

Offset: 0

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

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..730
Index entries for linear recurrences with constant coefficients, signature (22, 22, 22, 22, -253).

R:=PowerSeriesRing(Integers(), 20); Coefficients(R!( (1+x)*(1-x^5)/(1-23*x+275*x^5-253*x^6) )); // G. C. Greubel, May 16 2019

CoefficientList[Series[(1+x)*(1-x^5)/(1-23*x+275*x^5-253*x^6), {x, 0, 20}], x] (* G. C. Greubel, Jul 27 2017 *)
coxG[{5,253,-22}] (* The coxG program is at A169452 *) (* Harvey P. Dale, Aug 16 2018 *)

my(x='x+O('x^20)); Vec((1+x)*(1-x^5)/(1-23*x+275*x^5-253*x^6)) \\ G. C. Greubel, Jul 27 2017

((1+x)*(1-x^5)/(1-23*x+275*x^5-253*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)/(253*t^5 - 22*t^4 - 22*t^3 - 22*t^2 - 22*t + 1).

a(n) = 22*a(n-1)+22*a(n-2)+22*a(n-3)+22*a(n-4)-253*a(n-5). - Wesley Ivan Hurt, May 10 2021

cp's OEIS Frontend

A163440 Number of reduced words of length n in Coxeter group on 15 generators S_i with relations (S_i)^2 = (S_i S_j)^5 = I.

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A163441 Number of reduced words of length n in Coxeter group on 16 generators S_i with relations (S_i)^2 = (S_i S_j)^5 = I.

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A163451 Number of reduced words of length n in Coxeter group on 17 generators S_i with relations (S_i)^2 = (S_i S_j)^5 = I.

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A163452 Number of reduced words of length n in Coxeter group on 18 generators S_i with relations (S_i)^2 = (S_i S_j)^5 = 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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A163454 Number of reduced words of length n in Coxeter group on 20 generators S_i with relations (S_i)^2 = (S_i S_j)^5 = I.

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A163503 Number of reduced words of length n in Coxeter group on 21 generators S_i with relations (S_i)^2 = (S_i S_j)^5 = I.

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