

A370665


Number of standard hexagonal Young tableaux with n cells.


1



1, 1, 1, 3, 2, 6, 7, 16, 19, 63, 83, 172, 485, 833
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OFFSET

0,4


COMMENTS

A hexagonal Young diagram is a finite collection of hexagons or cells, arranged in center justified rows, with row lengths being either 1 or +1 of any adjacent rows above or below a given row, see illustration in links.
Reading the number of hexagons by row gives a integer composition (ordered partition) where differences between neighboring parts are in {1,1}. These diagrams can also be drawn with tangent circles on a hexagonal grid oriented pointy side up, see illustration link in A173258.
A standard hexagonal Young tableau is then created by filling the cells of a hexagonal Young diagram with numbers {1..n} such that all rows and downward diagonals form increasing sequences. For every hexagonal young diagram there is at least one hexagonal Young tableau.


LINKS



EXAMPLE

The integer composition [2,3,2] of 7, corresponds to the hexagonal Young diagram:
diagram tableau
0 0 1 2
0 0 0 > 3 4 5
0 0 6 7
Then filling in the cells sequentially by rows gives the tableau having rows [[1,2], [3,4,5], [6,7]] right diagonals [[3,6], [1,4,7], [2,5]] and left diagonals [[1,3], [2,4,6], [5,7]]; all of which contain increasing sequences.
The a(5) = 6 hexagonal Young tableaux with 5 cells are:
1 2 3 4 5 1 2 1 2 1 3 1 2 3 1 2 4
3 3 4 5 2 4 5 4 5 3 5
4 5


PROG

(Python) # see linked program


CROSSREFS

Cf. A173258 counts compositions where differences between neighboring parts are in {1,1}.


KEYWORD

nonn,more


AUTHOR



STATUS

approved



