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A230620
Number of permutations of [n] with at least two (possibly overlapping) occurrences of the consecutive step pattern {up}^2.
2
0, 0, 0, 0, 1, 9, 97, 983, 10616, 119932, 1441405, 18383351, 249155667, 3581896559, 54540748818, 877824410030, 14904605652001, 266431586957773, 5004557444810885, 98594548150006583, 2033673324306909868, 43845407809459639440, 986496730691143433269
OFFSET
0,6
LINKS
FORMULA
a(n) = Sum_{i=2..n-2} A162975(n,i).
a(n) ~ n!. - Vaclav Kotesovec, Sep 06 2014
EXAMPLE
a(4) = 1: 1234.
a(5) = 9: 12345, 12354, 12453, 13452, 21345, 23451, 31245, 41235, 51234.
a(6) = 97: 123456, 123465, 123546, ..., 631245, 641235, 651234.
a(7) = 983: 1234567, 1234576, 1234657, ..., 7631245, 7641235, 7651234.
MAPLE
b:= proc(u, o, t) option remember;
`if`(t=5, (u+o)!, `if`(u+o+t<4, 0,
add(b(u-j, o+j-1, [1, 1, 4, 4][t]), j=1..u)+
add(b(u+j-1, o-j, [2, 3, 5, 3][t]), j=1..o)))
end:
a:= n-> b(n, 0, 1):
seq(a(n), n=0..25);
MATHEMATICA
b[u_, o_, t_] := b[u, o, t] =
If[t == 5, (u + o)!, If[u + o + t < 4, 0,
Sum[b[u - j, o + j - 1, {1, 1, 4, 4}[[t]]], {j, 1, u}] +
Sum[b[u + j - 1, o - j, {2, 3, 5, 3}[[t]]], {j, 1, o}]]];
a[n_] := b[n, 0, 1];
a /@ Range[0, 25] (* Jean-François Alcover, Dec 22 2020, after Alois P. Heinz *)
CROSSREFS
Cf. A230621.
Sequence in context: A240780 A236672 A155699 * A155601 A241771 A180675
KEYWORD
nonn
AUTHOR
Alois P. Heinz, Oct 25 2013
STATUS
approved