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

Author

Chad Brewbaker, May 14 2013

Keywords

• nonn
• tabf

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.

Examples

			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;
		

Links

• Chad Brewbaker, Ruby program for A225725

Crossrefs

First column is A000248.

Row sums are: A000312.

Row lengths are A000793.

Number of nonzero elements of rows give A009490.

Cf. A222029.

Programs

Ruby

# See Brewbaker link.

Extensions

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