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 A346198 a(n) is the number of permutations on [n] with no strong fixed points but contains at least one small descent. 3
 0, 1, 1, 8, 43, 283, 2126, 17947, 168461, 1741824, 19684171, 241506539, 3198239994, 45482655683, 691471698917, 11193266251700, 192238116358427, 3491633681792507, 66875708261486766, 1347168876070616179, 28474546456352896021, 630130731702950549248, 14570725407559756078387, 351411668456841530417027 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,4 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 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 > 2, a(n) = b(n)-c(n) where b(n) = A052186(n-1), c(n) = A346189(n). EXAMPLE For n = 4, the a(4) = 8 permutations on [4] with no strong fixed points but has small descents: {([2, 1], [4, 3]), (2, [4, 3], 1), ([3, 2], 4, 1), (3, 4, [2, 1]), (4, 1, [3, 2]), (4, [2, 1], 3), ([4, 3], 1, 2), (<4, 3, 2, 1>)} []small descent, <>consecutive small descents. PROG (Python) See A346204. CROSSREFS Cf. A000255, A000166, A000153, A000261, A001909, A001910, A055790, A346189, A346199, A346204. Sequence in context: A117617 A111365 A199321 * A144039 A282189 A210125 Adjacent sequences: A346195 A346196 A346197 * A346199 A346200 A346201 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 April 1 23:16 EDT 2023. Contains 361717 sequences. (Running on oeis4.)