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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
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.
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
KEYWORD
nonn,tabf
AUTHOR
Chad Brewbaker, May 14 2013
EXTENSIONS
More terms, some terms corrected by Alois P. Heinz, Aug 17 2017
STATUS
approved