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A056841 Number of diagonal polyominoes with n cells. 3
1, 1, 2, 5, 15, 54, 212, 908, 4011, 18260 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

COMMENTS

Apparently the cells are circular blobs which must be connected diagonally and the polyominoes can be rotated by 90 degrees and turned over.

Also the number of essentially different (i.e. not related by reflections, translations or rotations) diagrams consisting of n nodes in Z^2 and n-1 horizontal or vertical edges of length 1 between pairs of nodes such that the resulting graph is connected (hence a tree). - Paul Boddington, Jul 27 2004

LINKS

Table of n, a(n) for n=1..10.

R. J. Mathar, Table of all such polyominoes with n <= 10 cells (gzipped)

R. J. Mathar, C++ program

M. Vicher, Polyforms

M. Vicher, The 15 5-celled diagonal polyominoes

M. Vicher, The 15 5-celled diagonal polyominoes

EXAMPLE

The polyominoes with 1, 2, 3 and 4 cells are

O..O...O...O.O..O....O....O.....O....O.O

....O...O...O....O....O....O...O.O..O.O.

.........O........O....O..O.O...O.......

...................O..O.................

CROSSREFS

See also A056840, A056787.

Sequence in context: A284729 A006966 A277175 * A185040 A208237 A107112

Adjacent sequences:  A056838 A056839 A056840 * A056842 A056843 A056844

KEYWORD

nonn,nice,more

AUTHOR

James A. Sellers, Aug 28 2000

EXTENSIONS

Description revised by N. J. A. Sloane, Jun 21 2001

a(10) from R. J. Mathar, Apr 10 2006

STATUS

approved

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Last modified February 24 18:24 EST 2018. Contains 299628 sequences. (Running on oeis4.)