|
|
A335472
|
|
Number of compositions of n matching the pattern (2,1,2).
|
|
8
|
|
|
0, 0, 0, 0, 0, 1, 3, 9, 25, 66, 165, 394, 914, 2068, 4607, 10093, 21818, 46592, 98498, 206452, 429670, 888818, 1829005, 3746802, 7645511, 15549306, 31534322, 63800562, 128823111, 259678348, 522715526, 1050957282, 2110953835, 4236623798, 8497083721, 17032615177
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
0,7
|
|
COMMENTS
|
Also the number of (1,2,2) or (2,2,1)-matching compositions.
We define a pattern to be a finite sequence covering an initial interval of positive integers. Patterns are counted by A000670 and ranked by A333217. A sequence S is said to match a pattern P if there is a not necessarily contiguous subsequence of S whose parts have the same relative order as P. For example, (3,1,1,3) matches (1,1,2), (2,1,1), and (2,1,2), but avoids (1,2,1), (1,2,2), and (2,2,1).
A composition of n is a finite sequence of positive integers summing to n.
|
|
LINKS
|
|
|
FORMULA
|
|
|
EXAMPLE
|
The a(5) = 1 through a(7) = 9 compositions:
(212) (1212) (313)
(2112) (2122)
(2121) (2212)
(11212)
(12112)
(12121)
(21112)
(21121)
(21211)
|
|
MATHEMATICA
|
Table[Length[Select[Join@@Permutations/@IntegerPartitions[n], MatchQ[#, {___, x_, ___, y_, ___, x_, ___}/; x>y]&]], {n, 0, 10}]
|
|
CROSSREFS
|
The version for prime indices is A335453.
These compositions are ranked by A335468.
The (1,2,1)-matching version is A335470.
The complement A335473 is the avoiding version.
The version for patterns is A335509.
Compositions are counted by A011782.
Non-unimodal compositions are counted by A115981 and ranked by A335373.
Combinatory separations are counted by A269134.
Patterns matched by compositions are counted by A335456.
Minimal patterns avoided by a standard composition are counted by A335465.
Compositions matching (1,2,3) are counted by A335514.
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|