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%I #52 Jul 23 2021 09:00:28
%S 0,0,2,6,34,214,1550,12730,116874,1187022,13219550,160233258,
%T 2100360778,29610224590,446789311934,7185155686666,122690711149290,
%U 2217055354281582,42269657477711198,847998698508705834,17857221256001240458,393839277313540073230,9078806210245773668990,218340709713567352161226
%N a(n) is the number of permutations on [n] with no strong fixed points or small descents.
%C A small descent in a permutation p is a position i such that p(i)-p(i+1)=1.
%C 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.
%D E. R. Berlekamp, J. H. Conway, and R. K. Guy, Winning Ways For Your Mathematical Plays, Vol. 1, CRC Press, 2001.
%H M. Lind, E. Fiorini, A. Woldar, and W. H. T. Wong, <a href="https://cs.uwaterloo.ca/journals/JIS/VOL24/Wong/wong31.html">On Properties of Pebble Assignment Graphs</a>, Journal of Integer Sequences, 24(6), 2020.
%F 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.
%e For n = 4, the a(4) = 6 permutations on [4] 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)}.
%o (Python) See A346204.
%Y Cf. A000255, A000166, A000153, A000261, A001909, A001910, A055790, A346198, A346199, A346204.
%K nonn
%O 1,3
%A _Eugene Fiorini_, _Jared Glassband_, _Garrison Lee Koch_, _Sophia Lebiere_, _Xufei Liu_, _Evan Sabini_, _Nathan B. Shank_, _Andrew Woldar_, Jul 09 2021
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