A225725 Triangle of transformation semigroup sizes generated by a single element.

1, 1, 3, 1, 10, 15, 2, 41, 129, 80, 6, 196, 1115, 1260, 510, 24, 20, 1057, 10395, 17780, 12840, 3744, 840, 6322, 105315, 258510, 264810, 135492, 47250, 4920, 0, 0, 504, 0, 420, 41393, 1160635, 4018000, 5318180, 3788400, 1837024, 513120, 38640, 0, 32256, 0, 26880, 0, 0, 2688

Offset

0,3

Comments

If you take the powers of a finite function you generate a lollipop graph. A222029 organizes the lollipops by cycle size. The table organized by total lollipop size with the tail included is this triangle.

Links

Table of n, a(n) for n=0..49.

Chad Brewbaker, Ruby program for A225725

Example

T(1,1) = #{[0]} = 1.
T(2,1) = #{[0,1], [0,0], [1,1]} = 3.
T(2,2) = #{[1,0]} = 1.
Triangle begins:
:    1;
:    1;
:    3,      1;
:   10,     15,      2;
:   41,    129,     80,      6;
:  196,   1115,   1260,    510,     24,    20;
: 1057,  10395,  17780,  12840,   3744,   840;
: 6322, 105315, 258510, 264810, 135492, 47250, 4920, 0, 0, 504, 0, 420;

Prog

(Ruby 1.9+) see link.

Crossrefs

First column is A000248.

Row sums are: A000312.

Row lengths are A000793.

Number of nonzero elements of rows give A009490.

Cf. A222029.

Sequence in context: A370258 A134991 A212930 * A095327 A225753 A210725

Adjacent sequences: A225722 A225723 A225724 * A225726 A225727 A225728

Keyword

nonn,tabf

Author

Chad Brewbaker, May 14 2013

Extensions

More terms, some terms corrected by Alois P. Heinz, Aug 17 2017

Status

approved