|
|
A263771
|
|
Triangle read by rows: T(n,k) (n>=0, k>=0) is the number of permutations of n and k occurrences of the pattern 312.
|
|
15
|
|
|
1, 1, 2, 5, 1, 14, 5, 4, 1, 42, 21, 23, 14, 12, 5, 3, 132, 84, 107, 82, 96, 55, 64, 37, 29, 22, 10, 0, 2, 429, 330, 464, 410, 526, 394, 475, 365, 360, 298, 281, 175, 206, 126, 93, 55, 23, 14, 13, 1, 2, 1430, 1287, 1950, 1918, 2593, 2225, 2858, 2489, 2682, 2401
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
0,3
|
|
COMMENTS
|
Also the number of permutations of n and k occurrences of either of the fixed pattern 132, 213, 231 (these are all connected by reverses and inverses).
|
|
LINKS
|
|
|
FORMULA
|
|
|
EXAMPLE
|
Triangle begins:
1;
1;
2;
5, 1;
14, 5, 4, 1;
42, 21, 23, 14, 12, 5, 3;
132, 84, 107, 82, 96, 55, 64, 37, 29, 22, 10, 0, 2;
...
|
|
MATHEMATICA
|
Join@@Array[Table[Length@Select[Permutations@Range@#, Length@Select[Subsets[#, {3}], Ordering@Ordering@#=={3, 1, 2}&]==k&], {k, 0, Binomial[#+1, 3]}]//.{a__, 0}:>{a}&, 8, 0] (* Giorgos Kalogeropoulos, Mar 26 2021 *)
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn,tabf
|
|
AUTHOR
|
|
|
EXTENSIONS
|
|
|
STATUS
|
approved
|
|
|
|