

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
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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.
Nonunimodal 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



