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 A346189 a(n) is the number of permutations on [n] with no strong fixed points or small descents. 3
 0, 0, 2, 6, 34, 214, 1550, 12730, 116874, 1187022, 13219550, 160233258, 2100360778, 29610224590, 446789311934, 7185155686666, 122690711149290, 2217055354281582, 42269657477711198, 847998698508705834, 17857221256001240458, 393839277313540073230, 9078806210245773668990, 218340709713567352161226 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,3 COMMENTS A small descent in a permutation p is a position i such that p(i)-p(i+1)=1. A strong fixed point is a fixed point (or splitter) p(k)=k such that p(i) < k for i < k and p(j) > k for j > k. REFERENCES E. R. Berlekamp, J. H. Conway, and R. K. Guy, Winning Ways For Your Mathematical Plays, Vol. 1, CRC Press, 2001. LINKS Table of n, a(n) for n=1..24. M. Lind, E. Fiorini, A. Woldar, and W. H. T. Wong, On Properties of Pebble Assignment Graphs, Journal of Integer Sequences, 24(6), 2020. FORMULA For n > 3, a(n) = b(n) - b(n-1) - Sum{i=4..n}(a(i-1)*b(n-i)) where b(n) = A000255(n-1) and b(0) = 1. EXAMPLE For n = 4, the a(4) = 6 permutations on  with no strong fixed points or small descents: {(2,3,4,1),(3,4,1,2),(4,1,2,3),(3,1,4,2),(2,4,1,3),(4,2,3,1)}. PROG (Python) See A346204. CROSSREFS Cf. A000255, A000166, A000153, A000261, A001909, A001910, A055790, A346198, A346199, A346204. Sequence in context: A003499 A279609 A253778 * A018953 A009199 A052824 Adjacent sequences: A346186 A346187 A346188 * A346190 A346191 A346192 KEYWORD nonn AUTHOR Eugene Fiorini, Jared Glassband, Garrison Lee Koch, Sophia Lebiere, Xufei Liu, Evan Sabini, Nathan B. Shank, Andrew Woldar, Jul 09 2021 STATUS approved

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Last modified May 30 07:09 EDT 2023. Contains 363045 sequences. (Running on oeis4.)