A225725 - OEIS

%I #41 Jan 06 2025 22:27:03

%S 1,1,3,1,10,15,2,41,129,80,6,196,1115,1260,510,24,20,1057,10395,17780,

%T 12840,3744,840,6322,105315,258510,264810,135492,47250,4920,0,0,504,0,

%U 420,41393,1160635,4018000,5318180,3788400,1837024,513120,38640,0,32256,0,26880,0,0,2688

%N Triangle of transformation semigroup sizes generated by a single element.

%C 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.

%H Chad Brewbaker, <a href="/A225725/a225725.txt">Ruby program for A225725</a>

%e T(1,1) = #{[0]} = 1.

%e T(2,1) = #{[0,1], [0,0], [1,1]} = 3.

%e T(2,2) = #{[1,0]} = 1.

%e Triangle begins:

%e :    1;

%e :    1;

%e :    3,      1;

%e :   10,     15,      2;

%e :   41,    129,     80,      6;

%e :  196,   1115,   1260,    510,     24,    20;

%e : 1057,  10395,  17780,  12840,   3744,   840;

%e : 6322, 105315, 258510, 264810, 135492, 47250, 4920, 0, 0, 504, 0, 420;

%o (Ruby) # See Brewbaker link.

%Y First column is A000248.

%Y Row sums are: A000312.

%Y Row lengths are A000793.

%Y Number of nonzero elements of rows give A009490.

%Y Cf. A222029.

%K nonn,tabf

%O 0,3

%A _Chad Brewbaker_, May 14 2013

%E More terms, some terms corrected by _Alois P. Heinz_, Aug 17 2017