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 A264461 Number of permutations of [n] with exactly two (possibly overlapping) occurrences of the generalized pattern 23-1. 2
 3, 23, 152, 984, 6460, 43626, 304939, 2211467, 16649780, 130097338, 1054226016, 8850736900, 76901730751, 690749091147, 6406953787268, 61300205459232, 604367205789092, 6133919028981542, 64027105979768111, 686736004045762143, 7562191796264603160 (list; graph; refs; listen; history; text; internal format)
 OFFSET 4,1 LINKS Alois P. Heinz, Table of n, a(n) for n = 4..500 EXAMPLE a(4) = 3: 2341, 3412, 3421. a(5) = 23: 13452, 14523, 14532, 23415, 23514, 23541, 24351, 25341, 32451, 34125, 34152, 34215, 35124, 35142, 35214, 35412, 35421, 42351, 43512, 43521, 52341, 53412, 53421. MAPLE b:= proc(u, o) option remember; `if`(u+o=0, 1, add( b(u-j, o+j-1), j=1..u) +add(convert(series( b(u+j-1, o-j)*x^u, x, 3), polynom), j=1..o)) end: a:= n-> coeff(b(n, 0), x, 2): seq(a(n), n=4..25); MATHEMATICA b[u_, o_] := b[u, o] = If[u+o == 0, 1, Sum[b[u-j, o+j-1], {j, 1, u}] + Sum[Series[b[u+j-1, o-j] x^u, {x, 0, 3}] // Normal, {j, 1, o}]]; a[n_] := Coefficient[b[n, 0], x, 2]; a /@ Range[4, 25] (* Jean-François Alcover, Sep 28 2020, after Maple *) CROSSREFS Column k=2 of A260670. Sequence in context: A232145 A079755 A197176 * A006184 A308677 A209011 Adjacent sequences: A264458 A264459 A264460 * A264462 A264463 A264464 KEYWORD nonn AUTHOR Alois P. Heinz, Nov 14 2015 STATUS approved

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Last modified September 23 13:49 EDT 2023. Contains 365551 sequences. (Running on oeis4.)