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A057542 Maximum cycle length in each permutation between A038776(1) and A038776(A000108(n)).

%I A057542 #7 Jun 13 2022 03:03:57
%S A057542 1,1,1,3,4,16,87,202,607,1441,4708,41888,44741,339108,1617551
%N A057542 Maximum cycle length in each permutation between A038776(1) and A038776(A000108(n)).
%H A057542 Sean A. Irvine, <a href="https://github.com/archmageirvine/joeis/blob/master/src/irvine/oeis/a057/A057542.java">Java program</a> (github)
%p A057542 map(lmax,Bf2DfBinTreePermutationCycleLengths(some_value)); (e.g. 10)
%p A057542 bf2df := s -> (btbf2df(binrev(s),0,1)/2); # btbf2df and binrev given in A038776
%p A057542 Bf2DfBinTreePermutationCycleLengths := proc(upto_n) local u,n,a,r,b; a := []; for n from 0 to upto_n do b := []; u := (binomial(2*n,n)/(n+1)); for r from 0 to u-1 do b := [op(b),1+CatalanRank(n,bf2df(CatalanUnrank(n,r)))]; od; a := [op(a),CycleLengths1(b)]; od; RETURN(a); end;
%p A057542 CycleLengths1 := b -> [[(nops(b)-convert(map(nops,convert(b,'disjcyc')),`+`)),`*`,1],op(map(nops,convert(b,'disjcyc')))];
%p A057542 last_term := proc(l) local n: n := nops(l); if(0 = n) then ([]) else (op(n,l)): fi: end:
%p A057542 lmax := proc(a) local e,z; z := 0; for e in a do if whattype(e) = list then e := last_term(e); fi; if e > z then z := e; fi; od; RETURN(z); end;
%Y A057542 Cycle lengths of permutation A038776 given in A038774.
%Y A057542 Cf. A057543, A057544, A057545.
%Y A057542 LCM's of all cycles: A060113.
%K A057542 nonn,more
%O A057542 0,4
%A A057542 _Antti Karttunen_, Sep 07 2000
%E A057542 a(11)-a(14) from _Sean A. Irvine_, Jun 13 2022