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 A242785 Number of permutations of [n] avoiding the consecutive step pattern given by the binary expansion of n, where 1=up and 0=down. 4
 1, 1, 2, 5, 21, 70, 450, 4326, 34944, 209863, 1573632, 21824925, 302273664, 2854894485, 60269056512, 1207441809209, 19346879737625, 252773481889854, 2918333808555034, 69792946997645295, 982945842995115000, 16085109561896603059, 402131210857811703926 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 LINKS Alois P. Heinz, Table of n, a(n) for n = 0..150 EXAMPLE a(4) = 21 because there are 4! = 24 permutations of {1,2,3,4} and only 3 of them do not avoid the consecutive step pattern up, down, down given by the binary expansion of 4 = 100_2: (1,4,3,2), (2,4,3,1), (3,4,2,1). MAPLE a:= proc(n) option remember; local b, m, r, h;       if n<2 then return 1 fi;       m:= iquo(n, 2, 'r'); h:= 2^ilog2(n);       b:= proc(u, o, t) option remember; `if`(u+o=0, 1,       `if`(t=m and r=0, 0, add(b(u-j, o+j-1, irem(2*t, h)), j=1..u))+       `if`(t=m and r=1, 0, add(b(u+j-1, o-j, irem(2*t+1, h)), j=1..o)))       end; forget(b);       b(n, 0, 0)     end: seq(a(n), n=0..30); MATHEMATICA a[n_] := a[n] = Module[{b, m, r, h},      If[n < 2, Return[1]]; {m, r} = QuotientRemainder[n, 2];      h = 2^(Length@IntegerDigits[n, 2] - 1);      b[u_, o_, t_] := b[u, o, t] = If[u + o == 0, 1,      If[t == m && r == 0, 0,           Sum[b[u - j, o + j - 1, Mod[2t, h]], {j, 1, u}]] +      If[t == m && r == 1, 0,           Sum[b[u + j - 1, o - j, Mod[2t+1, h]], {j, 1, o}]]];      b[n, 0, 0]]; a /@ Range[0, 30] (* Jean-François Alcover, Mar 23 2021, after Alois P. Heinz *) CROSSREFS Column k=0 of A242783. Main diagonal of A242784. Cf. A335308. Sequence in context: A000941 A000131 A328041 * A228385 A152801 A062297 Adjacent sequences:  A242782 A242783 A242784 * A242786 A242787 A242788 KEYWORD nonn AUTHOR Alois P. Heinz, May 22 2014 STATUS approved

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Last modified August 4 18:15 EDT 2021. Contains 346455 sequences. (Running on oeis4.)