A058159 -id:A058159 - cp's OEIS frontend

A034382 Number of labeled Abelian groups of order n.

1, 2, 3, 16, 30, 360, 840, 15360, 68040, 907200, 3991680, 159667200, 518918400, 14529715200, 163459296000, 4250979532800, 22230464256000, 1200445069824000, 6758061133824000, 405483668029440000

Offset: 1

Christian G. Bower

nonn

Max Alekseyev, Table of n, a(n) for n = 1..100
Hy Ginsberg, Totally Symmetric Quasigroups of Order 16, arXiv:2211.13204 [math.CO], 2022.
C. J. Hillar and D. Rhea. Automorphisms of finite Abelian groups. American Mathematical Monthly 114:10 (2007), 917-923. Preprint arXiv:math/0605185 [math.GR], 2006.
Sugarknri et al., Number of labeled Abelian groups of order n, Mathematics Stack Exchange, 2019.
Index entries for sequences related to groups

Cf. A000688, A034381, A034383, A058159.

a(n) = A058162(n) * n.

a(16) corrected by Max Alekseyev, Sep 12 2019

A058160 Triangle read by rows: T(n,k) is the number of labeled commutative monoids of order n with k idempotents and a fixed identity.

Original entry on oeis.org

1, 1, 1, 1, 6, 2, 4, 45, 36, 9, 6, 408, 648, 348, 76, 60, 7195, 13500, 11790, 5280, 1065, 120, 200016, 369930, 425280, 293640, 118890, 22566, 1920, 13811077, 14716716, 18035745, 16347660, 9953265, 3750516, 674611, 7560, 3405271616, 1024787568, 971651856, 999666920, 794967600, 445001424, 157962168, 27019896

Offset: 1

Christian G. Bower, Nov 14 2000

			Triangle begins:
   1;
   1,    1;,
   1,    6,     2;
   4,   45,    36,     9;
   6,  408,   648,   348,   76;
  60, 7195, 13500, 11790, 5280, 1065;
  ...

Andrew Howroyd, Table of n, a(n) for n = 1..55 (rows 1..10)
Index entries for sequences related to monoids

Row sums give A058156.
Column 1: A058162.
Main diagonal A058164.
Cf. A058142 (isomorphism classes), A058158, A058159.

T(n, k) = A058159(n, k)/n.

Terms a(30) and beyond from Andrew Howroyd, Feb 15 2022

A055512 Lattices with n labeled elements.

Original entry on oeis.org

1, 1, 2, 6, 36, 380, 6390, 157962, 5396888, 243179064, 13938711210, 987858368750, 84613071940452, 8597251494954564, 1020353444641839854, 139627532137612581090, 21788453795572514675760, 3840596246648027262079472, 758435490711709577216754642

Offset: 0

Jobst Heitzig (heitzig(AT)math.uni-hannover.de), Jul 03 2000

Sean A. Irvine, Table of n, a(n) for n = 0..19 (terms 0..18 from David Wasserman)
J. Heitzig and J. Reinhold, Counting finite lattices, preprint no. 298, Institut für Mathematik, Universität Hanover, Germany, 1999.
Sean A. Irvine, Java program (github).
J. Heitzig and J. Reinhold, Counting finite lattices, Algebra univers. 48, 43-53 (2002).
D. J. Kleitman and K. J. Winston, The asymptotic number of lattices, in: Combinatorial mathematics, optimal designs and their applications (Proc. Sympos. Combin. Math. and Optimal Design, Colorado State Univ., Fort Collins, Colo., 1978), Ann. Discrete Math. 6 (1980), 243-249.
Alan Veliz-Cuba and Reinhard Laubenbacher, Dynamics of semilattice networks with strongly connected dependency graph, Automatica (2019) Vol. 99, 167-174.
Index entries for "core" sequences

Cf. A006966, A001035. Main diagonal of A058159.

A058142 Triangle read by rows: number of commutative monoids of order n with k idempotents.

Original entry on oeis.org

1, 1, 1, 1, 3, 1, 2, 9, 6, 2, 1, 26, 30, 16, 5, 1, 98, 142, 111, 54, 15, 1, 455, 718, 713, 482, 215, 53, 3, 4018, 4277, 4637, 3919, 2414, 996, 222, 2, 101910, 36124, 32937, 31308, 24047, 13758, 5294, 1078, 1, 10054303, 708355, 290278, 260758, 229411, 164216, 88178, 31867, 5994

Offset: 1

Christian G. Bower, Nov 14 2000

			Triangle begins:
  1;
  1,  1;
  1,  3,   1;
  2,  9,   6,   2;
  1, 26,  30,  16, 5;
  1, 98, 142, 111, 54, 15;
  ...

Index entries for sequences related to monoids

Row sums give A058131.
Main diagonal: A006966.
Columns 1..2: A000688, A058143.
Cf. A058116, A058137, A058150, A058159, A058160.

a(30)-a(55) from Andrew Howroyd, Feb 15 2022

A058155 Number of labeled commutative monoids of order n.

Original entry on oeis.org

1, 4, 27, 376, 7430, 233340, 10013094, 618332080, 70437029472, 39048511536720

Offset: 1

Christian G. Bower, Nov 14 2000, corrected Dec 05 2003

Eric Postpischil, Posting to sci.math newsgroup, May 21 1990
Index entries for sequences related to monoids

Cf. A058156.

Row sums of A058159.

a(n) = A058156(n)*n.

a(8)-a(9) from Alex Meiburg, Oct 20 2021

a(10) from Andrew Howroyd, Feb 15 2022

A058157 Triangle read by rows: T(n,k) is the number of labeled monoids of order n with k idempotents.

Original entry on oeis.org

1, 2, 2, 3, 18, 12, 16, 180, 288, 140, 30, 2640, 6540, 8380, 3020, 480, 119610, 238200, 421020, 372360, 100362, 840, 25196052, 13786290, 26803000, 36174600, 22822674, 4768624, 22080, 48687313640, 2254725312, 2358499080, 3849768160, 3859581096, 1826525120, 305498328

Offset: 1

Christian G. Bower, Nov 14 2000

			Triangle begins:
   1;
   2,    2;
   3,   18,   12;
  16,  180,  288,  140;
  30, 2640, 6540, 8380, 3020;
  ...

Index entries for sequences related to monoids

Row sums give A058153.
Column 1: A034383.
Main diagonal is A351731.
Cf. A058137 (isomorphism classes), A058158, A058159 (commutative), A058166.

T(n,k) = A058158(n,k)*n.

a(30)-a(36) from Andrew Howroyd, Feb 15 2022

A173488 Partial sums of A055512.

Original entry on oeis.org

1, 2, 4, 10, 46, 426, 6816, 164778, 5561666, 248740730, 14187451940, 1002045820690, 85615117761142, 8682866612715706, 1029036311254555560, 140656568448867136650, 21929110364021381812410, 3862525357012048643891882, 762298016068721625860646524

Offset: 0

Jonathan Vos Post, Feb 19 2010

Partial sums of the number of lattices with n labeled elements. After a(0) = 1, always even, hence the only prime in the partial sum is 2. The subsequence of semiprimes begins 4, 10, 46.

Cf. A055512, A006966, A001035, Main diagonal of A058159.

Cases[Import["https://oeis.org/A055512/b055512.txt", "Table"], {, }][[All, 2]] // Accumulate (* Jean-François Alcover, Jan 02 2020 *)

a(n) = Sum_{i=0..n} A055512(i).

a(17)-a(18) from Jean-François Alcover, Jan 02 2020

cp's OEIS Frontend

A034382 Number of labeled Abelian groups of order n.

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A058160 Triangle read by rows: T(n,k) is the number of labeled commutative monoids of order n with k idempotents and a fixed identity.

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A055512 Lattices with n labeled elements.

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A058142 Triangle read by rows: number of commutative monoids of order n with k idempotents.

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A058155 Number of labeled commutative monoids of order n.

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A058157 Triangle read by rows: T(n,k) is the number of labeled monoids of order n with k idempotents.

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A173488 Partial sums of A055512.

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