cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-4 of 4 results.

A359520 Number of free holey polyominoes of n cells with simply-connected interiors.

Original entry on oeis.org

0, 0, 0, 0, 0, 0, 1, 5, 35, 179, 909, 4285, 19702, 88040, 386826, 1674852, 7174436, 30462009
Offset: 1

Views

Author

John Mason, Jan 04 2023

Keywords

Examples

			a(7) = 1 because of the holey heptomino.

Crossrefs

Cf. A000104, A000105, A001419, A342537, A359519.

Formula

a(n) = A342537(n) - A000104(n) (simply connected polyominoes minus unholey polyominoes).

A359519 Number of free polyominoes of n cells with multiply-connected interiors.

Original entry on oeis.org

0, 0, 0, 0, 0, 0, 0, 1, 2, 16, 70, 378, 1772, 8456, 38623, 174400, 771944, 3378937
Offset: 1

Views

Author

John Mason, Jan 04 2023

Keywords

Examples

			a(8) = 1 because of:
OOO
O O
OOO

Crossrefs

Cf. A000104, A000105, A001419, A342537, A359520.

Formula

a(n) = A000105(n) - A342537(n) (all free polyominoes minus simply-connected interior polyominoes).

A216819 Number of simply 8-connected polyominoes of site-perimeter n.

Original entry on oeis.org

1, 0, 2, 4, 12, 32, 110, 340, 1209, 4256, 15974, 60232
Offset: 4

Views

Author

N. J. A. Sloane, Sep 20 2012

Keywords

Links

Crossrefs

Cf. A216818 (no holes), A216820 (any holes).
A342537 counts free (rather than fixed) polyominoes with given area (rather than site-perimeter).

A342538 Number of free polyominoes with n cells having simply-connected interiors such that no smaller polyomino has the same bracelet.

Original entry on oeis.org

1, 0, 1, 2, 4, 7, 17, 40, 101, 259, 671, 1741, 4689, 12511, 33603, 91249
Offset: 1

Views

Author

John Mason, Allan C. Wechsler, Mar 15 2021

Keywords

Comments

Consider only the corners of the polygon that forms the border of the polyomino. Then build the bracelet of black and white beads by following the border of the polygon in a clockwise direction, adding a black bead for each right-turning right angle, and a white bead for each left-turning right angle. Count in this sequence only polyominoes for which no smaller polyomino has the same bracelet. Note 2 polyominoes of the same size having the same bracelet will count as 2.

Examples

			a(2) is 0 as the domino has bracelet BBBB, which is the same as the monomino.

Crossrefs

Cf. A342537.
Showing 1-4 of 4 results.

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

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