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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 February 29 23:09 EST 2024. Contains 370428 sequences. (Running on oeis4.)