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 1-3 of 3 results.

A268416 Number of aligned free polyominoes that will fit in a square of size n X n.

Original entry on oeis.org

1, 4, 35, 1280, 262292, 205515653, 592830103236
Offset: 1

Views

Author

John Mason, Feb 04 2016

Keywords

Comments

a(n) is the number of free polyominoes that have both width and height <= n. Compare this to Craig Knecht's A268311 which has both height and width = n. The word "aligned" in the title refers to the restriction that the polyominoes have edges parallel to the sides of the square, in contrast with A268427.

Crossrefs

Cf. A268311, A268371, A268427.

Formula

a(n) = Sum_{i=1..n*(n+1)/2} A268371(i). - John Mason, Sep 11 2024

Extensions

a(6) from Talmon Silver, Jul 29 2020
a(7) from John Mason, Sep 11 2024

A328020 Number of distinct tilings of an n X n square with free n-polyominoes.

Original entry on oeis.org

1, 1, 2, 22, 515, 56734, 19846102, 23437350133
Offset: 1

Views

Author

Jeff Bowermaster, Oct 01 2019

Keywords

Links

Crossrefs

Cf. A172477, A268427, A291806.

Extensions

a(7) from Peter Kagey, Oct 10 2019, based on the Stack Exchange link.
a(8) from Christian Sievers, Oct 13 2019, based on the Stack Exchange link.

A339848 Number of distinct free polyominoes that fit in an n X n square but are not a proper sub-polyomino of any polyomino that fits in the square.

Original entry on oeis.org

1, 1, 1, 1, 3, 6, 16, 27, 44, 70
Offset: 1

Views

Author

Talmon Silver, Dec 19 2020

Keywords

Comments

A polyomino A is a proper sub-polyomino of B if one or more cells can be added to A to form B.
Except for the n X n polyomino that fills the square all of the other polyominoes must have their edges aligned at an angle to the sides of the square.
This counts the minimum subset of polyominoes needed to produce A268427 - that sequence counts the sub-polyominoes of this sequence.

Examples

			For n=1, 2, 3, 4 the only polyominoes are the n X n polyominoes. Thus, a(1)=a(2)=a(3)=a(4)=1.
For n=5 and n=6 all of the other polyominoes are shown in the links.

Links

Crossrefs

Cf. A268427.
Showing 1-3 of 3 results.

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