A378015 - OEIS

The OEIS is supported by the many generous donors to the OEIS Foundation.

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).

Other ways to Give

A378015

Triangle read by rows: T(n,k) = number of free hexagonal polyominoes with n cells, where the maximum number of collinear cell centers on any line in the plane is k.

1, 0, 1, 0, 2, 1, 0, 4, 2, 1, 0, 2, 16, 3, 1, 0, 3, 52, 23, 3, 1, 0, 0, 169, 129, 30, 4, 1, 0, 0, 477, 740, 187, 39, 4, 1, 0, 0, 1245, 3729, 1274, 270, 48, 5, 1, 0, 0, 2750, 17578, 7785, 1948, 364, 59, 5, 1, 0, 0, 5380, 75827, 46045, 12895, 2840, 488, 70, 6, 1

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

OFFSET

1,5

COMMENTS

The row sums are the total number of free hexagon polyominoes with n cells.

LINKS

Table of n, a(n) for n=1..66.

Dave Budd, Python code for a hex lattice.

EXAMPLE

| k

n | 1 2 3 4 5 6 7 8 9 10 Total

---------------------------------------------------------------------------------------

1 | 1 1

2 | 0 1 1

3 | 0 2 1 3

4 | 0 4 2 1 7

5 | 0 2 16 3 1 22

6 | 0 3 52 23 3 1 82

7 | 0 0 169 129 30 4 1 333

8 | 0 0 477 740 187 39 4 1 1448

9 | 0 0 1245 3729 1274 270 48 5 1 6572

10 | 0 0 2750 17578 7785 1948 364 59 5 1 30490

The T(5,2)=2 hexagon polyominoes are:

# # #

# # # #

# # #

CROSSREFS

Cf. A000228 (row sums).

Cf. A377942 (similar collinear cell constraint for square polyominoes).

Cf. A377756 (specific case for the cumulative value for k<=3 i.e. T(n,1)+T(n,2)+T(n,3) ).

Cf. A378014 (collinear cell constraint applied only to cells on lattice lines).

Sequence in context: A062296 A249343 A369206 * A378014 A355756 A140649

Adjacent sequences: A378012 A378013 A378014 * A378016 A378017 A378018

KEYWORD

nonn,tabl

AUTHOR

Dave Budd, Nov 14 2024

STATUS

approved