cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-9 of 9 results.

A229644 Cogrowth function of the group Baumslag-Solitar(2,2).

Original entry on oeis.org

1, 4, 28, 244, 2396, 25324, 281140, 3232352, 38151196, 459594316, 5628197948, 69859456440, 876985904276, 11115789165888, 142066687799680, 1828884017527504, 23694360858872604, 308714491495346028, 4042605442981407388, 53178663502737007352
Offset: 0

Views

Author

Murray Elder, Sep 27 2013

Keywords

Comments

a(n) is the number of words of length 2n in the letters a,a^{-1},t,t^{-1} that equal the identity of the group BS(2,2)=.

Examples

			For n=1 there are 4 words of length 2 equal to the identity: aa^{-1}, a^{-1}a, tt^{-1}, t^{-1}t.

Links

Crossrefs

The cogrowth sequences for BS(N,N) for N = 1..10 are A002894, A229644, A229645, A229646, A229647, A229648, A229649, A229650, A229651, A229652.

A229645 Cogrowth function of the group Baumslag-Solitar(3,3).

Original entry on oeis.org

1, 4, 28, 232, 2108, 20364, 205696, 2149956, 23087260, 253400200, 2831688428, 32121034928, 368996930720, 4284878088040, 50221403053556, 593400572917032, 7061298334083484, 84555438345880932, 1018170456984477856, 12321676227943830972
Offset: 0

Views

Author

Murray Elder, Sep 27 2013

Keywords

Comments

a(n) is the number of words of length 2n in the letters a,a^{-1},t,t^{-1} that equal the identity of the group BS(3,3)=.

Examples

			For n=1 there are 4 words of length 2 equal to the identity: aa^{-1}, a^{-1}a, tt^{-1}, t^{-1}t.

Links

Crossrefs

The cogrowth sequences for BS(N,N) for N = 1..10 are A002894, A229644, A229645, A229646, A229647, A229648, A229649, A229650, A229651, A229652.

A229646 Cogrowth function of the group Baumslag-Solitar(4,4).

Original entry on oeis.org

1, 4, 28, 232, 2092, 19884, 196096, 1988424, 20611116, 217526524, 2330681348, 25296553088, 277653104800, 3077568629256, 34410056828392, 387725845018512, 4399241841920428, 50228061806093020, 576729989899675348
Offset: 0

Views

Author

Murray Elder, Sep 27 2013

Keywords

Comments

a(n) is the number of words of length 2n in the letters a,a^{-1},t,t^{-1} that equal the identity of the group BS(4,4)=.

Examples

			For n=1 there are 4 words of length 2 equal to the identity: aa^{-1}, a^{-1}a, tt^{-1}, t^{-1}t.

Links

Crossrefs

The cogrowth sequences for BS(N,N) for N = 1..10 are A002894, A229644, A229645, A229646, A229647, A229648, A229649, A229650, A229651, A229652.

A229647 Cogrowth function of the group Baumslag-Solitar(5,5).

Original entry on oeis.org

1, 4, 28, 232, 2092, 19864, 195376, 1971932, 20303084, 212400232, 2251379688, 24129199208, 261067326544, 2848016992032, 31295785633532, 346126420439512, 3850363854970476, 43057199315715676, 483795646775017312, 5459770924922887392
Offset: 0

Views

Author

Murray Elder, Sep 27 2013

Keywords

Comments

a(n) is the number of words of length 2n in the letters a,a^{-1},t,t^{-1} that equal the identity of the group BS(5,5)=.

Examples

			For n=1 there are 4 words of length 2 equal to the identity: aa^{-1}, a^{-1}a, tt^{-1}, t^{-1}t.

Links

Crossrefs

The cogrowth sequences for BS(N,N) for N = 1..10 are A002894, A229644, A229645, A229646, A229647, A229648, A229649, A229650, A229651, A229652.

A229649 Cogrowth function of the group Baumslag-Solitar(7,7).

Original entry on oeis.org

1, 4, 28, 232, 2092, 19864, 195352, 1970896, 20275692, 211825564, 2240852928, 23952708696, 258285519688, 2806105225928, 30685515254240, 337472968923532, 3730218568024236, 41417273400310152, 461722437389957236, 5166105817092273412
Offset: 0

Views

Author

Murray Elder, Sep 27 2013

Keywords

Comments

a(n) is the number of words of length 2n in the letters a,a^{-1},t,t^{-1} that equal the identity of the group BS(7,7)=.

Examples

			For n=1 there are 4 words of length 2 equal to the identity: aa^{-1}, a^{-1}a, tt^{-1}, t^{-1}t.

Links

Crossrefs

The cogrowth sequences for BS(N,N) for N = 1..10 are A002894, A229644, A229645, A229646, A229647, A229648, A229649, A229650, A229651, A229652.

A229650 Cogrowth function of the group Baumslag-Solitar(8,8).

Original entry on oeis.org

1, 4, 28, 232, 2092, 19864, 195352, 1970896, 20275660, 211823836, 2240798048, 23951367224, 258257552968, 2805581350056, 30676425237024, 337324008602512, 3727882769574860, 41381900166952348, 461201577710442388, 5158610797198820800
Offset: 0

Views

Author

Murray Elder, Sep 27 2013

Keywords

Comments

a(n) is the number of words of length 2n in the letters a,a^{-1},t,t^{-1} that equal the identity of the group BS(8,8)=.

Examples

			For n=1 there are 4 words of length 2 equal to the identity: aa^{-1}, a^{-1}a, tt^{-1}, t^{-1}t.

Links

Crossrefs

The cogrowth sequences for BS(N,N) for N = 1..10 are A002894, A229644, A229645, A229646, A229647, A229648, A229649, A229650, A229651, A229652.

A229651 Cogrowth function of the group Baumslag-Solitar(9,9).

Original entry on oeis.org

1, 4, 28, 232, 2092, 19864, 195352, 1970896, 20275660, 211823800, 2240795888, 23951292204, 258255572584, 2805537209648, 30675548482880, 337307986673572, 3727607821613388, 41377406950962504, 461130952671387592, 5157535231753964268
Offset: 0

Views

Author

Murray Elder, Sep 28 2013

Keywords

Comments

a(n) is the number of words of length 2n in the letters a,a^{-1},t,t^{-1} that equal the identity of the group BS(9,9)=.

Examples

			For n=1 there are 4 words of length 2 equal to the identity: aa^{-1}, a^{-1}a, tt^{-1}, t^{-1}t.

Links

Crossrefs

The cogrowth sequences for BS(N,N) for N = 1..10 are A002894, A229644, A229645, A229646, A229647, A229648, A229649, A229650, A229651, A229652.

A229652 Cogrowth function of the group Baumslag-Solitar(10,10).

Original entry on oeis.org

1, 4, 28, 232, 2092, 19864, 195352, 1970896, 20275660, 211823800, 2240795848, 23951289564, 258255473032, 2805534386256, 30675481454184, 337306578693652, 3727580774618060, 41376921517941032, 461122691909043112, 5157400529078643552
Offset: 0

Views

Author

Murray Elder, Sep 28 2013

Keywords

Comments

a(n) is the number of words of length 2n in the letters a,a^{-1},t,t^{-1} that equal the identity of the group BS(10,10)=.

Examples

			For n=1 there are 4 words of length 2 equal to the identity: aa^{-1}, a^{-1}a, tt^{-1}, t^{-1}t.

Links

Crossrefs

The cogrowth sequences for BS(N,N) for N = 1..10 are A002894, A229644, A229645, A229646, A229647, A229648, A229649, A229650, A229651, A229652.

A307468 Cogrowth sequence for the Heisenberg group.

Original entry on oeis.org

1, 4, 28, 232, 2156, 21944, 240280, 2787320, 33820044, 424925872, 5486681368, 72398776344, 972270849512, 13247921422480, 182729003683352, 2546778437385032, 35816909974343308, 507700854900783784, 7246857513425470288, 104083322583897779656
Offset: 0

Views

Author

Igor Pak, Apr 09 2019

Keywords

Comments

This is the number of words of length 2n in the letters x,x^{-1},y,y^{-1} that equal the identity of the Heisenberg group H=.
Also, this is the number of closed walks of length 2n on the square lattice enclosing algebraic area 0 [Béguin et al.]. - Andrey Zabolotskiy, Sep 15 2021

Examples

			For n=1 the a(1)=4 words are x^{-1}x, xx^{-1}, y^{-1}y, yy^{-1}.

Links

Crossrefs

Related cogrowth sequences: Z A000984, Z^2 A002894, Z^3 A002896, (Z/kZ)^*2 for k = 2..5: A126869, A047098, A107026, A304979, Richard Thompson's group F A246877. The cogrowth sequences for BS(N,N) for N = 2..10 are A229644, A229645, A229646, A229647, A229648, A229649, A229650, A229651, A229652.
Cf. A352838, A178106.

Formula

Asymptotics: a(n) ~ (1/2) * 16^n * n^(-2).
Showing 1-9 of 9 results.

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

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