proposed

approved

editing

proposed

Andrew Howroyd, <a href="/A058160/b058160.txt">Table of n, a(n) for n = 1..55</a> (rows 1..10)

Cf. A058142 (isomorphism classes), A058158, A058159.

Terms a(30)-a(45) and beyond from Andrew Howroyd, Feb 15 2022

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

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

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

1; 1,1; 1,6,2; 4,45,36,9; 6,408,648,348,76; ...

Triangle begins:

1;

1, 1;,

1, 6, 2;

4, 45, 36, 9;

6, 408, 648, 348, 76;

60, 7195, 13500, 11790, 5280, 1065;

...

a(n, k)=A058159(n, k)/n. Row sums give A058156. Column 1: A058162. Main diagonal A058164.

Row sums give A058156.

Column 1: A058162.

Main diagonal A058164.

Cf. A058159.

nonn,tabl,more

a(30)-a(45) from Andrew Howroyd, Feb 15 2022

approved

editing

_Christian G. Bower (bowerc(AT)usa.net), _, Nov 14 2000

<a href="/Sindx_index/Mo.html#monoids">Index entries for sequences related to monoids</a>

<a href="/Sindx_Mo.html#monoids">Index entries for sequences related to monoids</a>

nonn,tabl,more,new

<a href="http://www.research.att.com/~njas/sequences/Sindx_Mo.html#monoids">Index entries for sequences related to monoids</a>

nonn,tabl,more,new

Triangle: Labeled commutative monoids of order n with k idempotents with a fixed identity.

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

1,5

<a href="http://www.research.att.com/~njas/sequences/Sindx_Mo.html#monoids">Index entries for sequences related to monoids</a>

1; 1,1; 1,6,2; 4,45,36,9; 6,408,648,348,76; ...

a(n, k)=A058159(n, k)/n. Row sums give A058156. Column 1: A058162. Main diagonal A058164.

nonn,tabl,more

Christian G. Bower (bowerc(AT)usa.net), Nov 14 2000

approved