A378014 - OEIS

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A378014

Triangle read by rows: T(n,k) = number of free hexagonal polyominoes with n cells, where the maximum number of cells on any lattice line is k. The term "lattice line" here means a line running through the cell centers and midpoints of their sides.

1, 0, 1, 0, 2, 1, 0, 4, 2, 1, 0, 3, 15, 3, 1, 0, 5, 50, 23, 3, 1, 0, 1, 171, 126, 30, 4, 1, 0, 1, 506, 710, 187, 39, 4, 1, 0, 1, 1459, 3520, 1268, 270, 48, 5, 1, 0, 1, 3792, 16617, 7703, 1948, 364, 59, 5, 1, 0, 1, 9292, 72870, 45099, 12885, 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 hexagonal 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 3 15 3 1 22

6 | 0 5 50 23 3 1 82

7 | 0 1 171 126 30 4 1 333

8 | 0 1 506 710 187 39 4 1 1448

9 | 0 1 1459 3520 1268 270 48 5 1 6572

10 | 0 1 3792 16617 7703 1948 364 59 5 1 30490

The T(4,2)=4 hexagon polyominoes are:

# # # # # #

# # # # # # # #

# #

CROSSREFS

Row sums are A000228.

Cf. A377941, A378015.

Sequence in context: A249343 A369206 A378015 * A355756 A140649 A290222

Adjacent sequences: A378011 A378012 A378013 * A378015 A378016 A378017

KEYWORD

nonn,tabl

AUTHOR

Dave Budd, Nov 14 2024

STATUS

approved