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A225725 Triangle of transformation semigroup sizes generated by a single element. 2
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 (list; graph; refs; listen; history; text; internal format)
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: A176740 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

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Last modified May 25 10:48 EDT 2020. Contains 334592 sequences. (Running on oeis4.)