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 A177478 Permutations avoiding the consecutive patterns 4312 and 4213. 4
 1, 1, 2, 6, 22, 100, 540, 3388, 24248, 195048, 1742860, 17127880, 183617280, 2132433940, 26669752928, 357375269160, 5108084756320, 77574769941760, 1247401873186560, 21172559509803520, 378282904982091200, 7096584257305845120, 139471475802695196160 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 COMMENTS a(n) gives the number of permutations of [n] which avoid both the pattern 4312 and 4213 consecutively.  Also the number avoiding the pairs {2134, 3124}, {1243, 1342}, or {3421, 2431} (by symmetry). This can also be considered avoiding a partially ordered pattern:  Suppose p0, s+t-1, 1)..o))     end: a:= n-> b(0, n, 0, 0): seq(a(n), n=0..25);  # Alois P. Heinz, Oct 25 2013 MATHEMATICA b[u_, o_, s_, t_] := b[u, o, s, t] = If[u+o == 0, 1, Sum[b[u-j, o+j-1, t, j], {j, 1, u}] + Sum[b[u+j-1, o-j, 0, 0], {j, If[s > 0, s+t-1, 1], o}]]; a[n_] := b[0, n, 0, 0]; a /@ Range[0, 25] (* Jean-François Alcover, Nov 03 2020, after Alois P. Heinz *) CROSSREFS Cf. A117226, A117156. Sequence in context: A012266 A009468 A088819 * A052517 A245119 A012270 Adjacent sequences:  A177475 A177476 A177477 * A177479 A177480 A177481 KEYWORD nonn AUTHOR Signy Olafsdottir (signy06(AT)ru.is), May 09 2010 EXTENSIONS More terms, succinct title, additional comments, new references from Andrew Baxter, Jan 21 2011 STATUS approved

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Last modified April 22 07:26 EDT 2021. Contains 343163 sequences. (Running on oeis4.)