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 A231228 Number of permutations of [n] with exactly one occurrence of one of the consecutive patterns 123, 1432, 2431, 3421. 2
 0, 0, 0, 1, 9, 59, 358, 2235, 14658, 103270, 778451, 6315499, 54733657, 507655301, 5003179539, 52430810493, 580611272956, 6796733911852, 83658527086447, 1083027034959367, 14678725047527255, 208344799726820123, 3084495765476262875, 47646333262275943521 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,5 LINKS Alois P. Heinz, Table of n, a(n) for n = 0..200 FORMULA a(n) ~ c * (2/Pi)^n * n! * n, where c = 3.08472832460941829086964816782... . - Vaclav Kotesovec, Aug 28 2014 EXAMPLE a(3) = 1: 123. a(4) = 9: 1243, 1342, 1432, 2134, 2341, 2431, 3124, 3421, 4123. a(5) = 59: 12435, 12534, 13245, ..., 53124, 53421, 54123. a(6) = 358: 124365, 125364, 125463, ..., 653124, 653421, 654123. MAPLE b:= proc(u, o, t) option remember;       `if`(t=7, 0, `if`(u+o=0, `if`(t in [4, 5, 6], 1, 0),       add(b(u+j-1, o-j, [2, 5, 2, 5, 7, 5][t]), j=1..o)+       add(b(u-j, o+j-1, [1, 3, 4, 4, 6, 7][t]), j=1..u)))     end: a:= n-> b(n, 0, 1): seq(a(n), n=0..25); MATHEMATICA b[u_, o_, t_] := b[u, o, t] = If[t==7, 0, If[u+o==0, If[4 <= t <= 6, 1, 0],       Sum[b[u + j - 1, o - j, {2, 5, 2, 5, 7, 5}[[t]]], {j, 1, o}] +       Sum[b[u - j, o + j - 1, {1, 3, 4, 4, 6, 7}[[t]]], {j, 1, u}]]]; a[n_] := b[n, 0, 1]; a /@ Range[0, 25] (* Jean-François Alcover, Jan 03 2021, after Alois P. Heinz *) CROSSREFS Column k=1 of A231210. Sequence in context: A174654 A027249 A026717 * A198847 A059356 A039929 Adjacent sequences:  A231225 A231226 A231227 * A231229 A231230 A231231 KEYWORD nonn AUTHOR Alois P. Heinz, Nov 05 2013 STATUS approved

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Last modified August 12 22:46 EDT 2022. Contains 356077 sequences. (Running on oeis4.)