A387336 - OEIS

A387336

Triangle read by rows: T(n,k) is the number of length n words over an n-ary alphabet such that the maximal cardinality of C is k, where C is a subset of the alphabet such that all letters in C appear in weakly increasing order within the word.

1, 0, 1, 0, 3, 1, 0, 16, 10, 1, 0, 111, 123, 21, 1, 0, 956, 1681, 451, 36, 1, 0, 9797, 25691, 9929, 1183, 55, 1, 0, 116089, 436458, 230700, 37661, 2556, 78, 1, 0, 1559315, 8176511, 5711323, 1214767, 110333, 4861, 105, 1

(list; table; graph; refs; listen; history; text; internal format)

OFFSET

0,5

LINKS

Table of n, a(n) for n=0..44.

John Tyler Rascoe, Python code.

EXAMPLE

Triangle begins:

k=0 1 2 3 4 5 6

n=0 1;

n=1 0, 1;

n=2 0, 3, 1;

n=3 0, 16, 10, 1;

n=4 0, 111, 123, 21, 1;

n=5 0, 956, 1681, 451, 36, 1;

n=6 0, 9797, 25691, 9929, 1183, 55, 1;

...

T(2,1) = 3 counts: (1,1), (2,1), (2,2).

T(2,2) = 1 counts: (1,2).

The word (2,3,1,3,4,1,2,6,2,6) over the alphabet {1,2,3,4,5,6} has maximal subset C = {3,4,6}.

PROG

(Python) # see links

CROSSREFS

Cf. A000312 (row sums), A014105 (second diagonal).

Cf. A385604, A386891.

Sequence in context: A243098 A360177 A241981 * A147723 A110518 A246049

Adjacent sequences: A387333 A387334 A387335 * A387337 A387338 A387339

KEYWORD

nonn,tabl,more

AUTHOR

John Tyler Rascoe, Aug 26 2025

STATUS

approved