|
|
A264452
|
|
Number of permutations of [n] with exactly three (possibly overlapping) occurrences of the generalized pattern 12-3.
|
|
2
|
|
|
1, 12, 103, 811, 6273, 48806, 386041, 3122069, 25900188, 220791812, 1935811756, 17461471292, 162038542377, 1546528485770, 15174625184321, 152994813139537, 1584120732683571, 16834244135840106, 183496533502593453, 2050337555698723711, 23470542944212951050
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
4,2
|
|
LINKS
|
|
|
EXAMPLE
|
a(4) = 1: 1234.
a(5) = 12: 12534, 12543, 13245, 13425, 13452, 21345, 23145, 23415, 23451, 31245, 41235, 51234.
|
|
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^(o-j), x, 4), polynom), j=1..o))
end:
a:= n-> coeff(b(n, 0), x, 3):
seq(a(n), n=4..25);
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|