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.

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A357647 a(n) is the number of free unholey polyominoes of n cells with 90-degree rotational symmetry and no other.

Original entry on oeis.org

0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 2, 2, 0, 0, 7, 7, 0, 0, 22, 24, 0, 0, 71, 82, 0, 0, 239, 280, 0, 0, 817, 970, 0, 0, 2841, 3403, 0, 0, 10027, 12064, 0, 0, 35800, 43193, 0, 0, 129007, 156011, 0, 0, 468541, 567664, 0, 0, 1713174
Offset: 1

Views

Author

John Mason, Oct 10 2022

Keywords

Crossrefs

Cf. A000104, A144553.

A357648 Number of polyominoes with n cells that have the symmetry group D_8 and are without holes.

Original entry on oeis.org

1, 0, 0, 1, 1, 0, 0, 0, 2, 0, 0, 1, 2, 0, 0, 1, 3, 0, 0, 1, 5, 0, 0, 2, 8, 0, 0, 2, 13, 0, 0, 3, 20, 0, 0, 5, 33, 0, 0, 6, 55, 0, 0, 10, 93, 0, 0, 13, 157, 0, 0, 22, 268, 0, 0, 30, 461, 0, 0, 51, 801, 0, 0, 71, 1396, 0, 0, 124, 2459, 0, 0, 175, 4329, 0, 0, 317, 7696
Offset: 1

Views

Author

John Mason, Oct 10 2022

Keywords

Crossrefs

Cf. A000104, A142886.

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).

A057409 Number of self-avoiding polygons of area n with any number of (self-avoiding polygon) holes on square lattice (not allowing rotations).

Original entry on oeis.org

1, 2, 6, 19, 63, 216, 756, 2685, 9650, 35018, 128084, 471623, 1746492, 6499356, 24290272, 91123171, 342984175, 1294829776, 4901319978, 18597856445, 70723784744, 269486503694, 1028736811230, 3933715966653
Offset: 1

Views

Author

N. J. A. Sloane, Aug 30 2000

Keywords

Links

Crossrefs

Cf. A006724 (no holes, first differs at n=8), A057406, A057407, A057408 (resp. 1, 2, 3 holes); A001168 (any holes, first differs at n=7); A088702 (by perimeter); A000104 (no holes, rotations and reflections allowed).

A384428 a(n) is the minimal area of a polyomino without holes having a product of edge lengths equal to n, or 0 if no solution is possible.

Original entry on oeis.org

1, 0, 4, 2, 7, 0, 10, 5, 3, 0, 16, 4, 19, 0, 6, 4, 25, 0, 28, 6, 9, 0, 34, 5, 5, 0, 6, 9, 43, 0, 46, 6, 15, 0, 8, 5, 55, 0, 18, 6, 61, 0, 64, 15, 8, 0, 70, 6, 7, 0
Offset: 1

Views

Author

Gordon Hamilton, May 28 2025

Keywords

Comments

Good sequence for elementary school students learning multiplication.
If p is the largest prime factor dividing n, then a(n) >= p because there needs to be at least one edge of length k*p for some k>=1.
a(51) > 21. - Sean A. Irvine, Jun 13 2025

Examples

			a(36)=5 because the V pentomino is the smallest polyomino whose edges multiply together to give 36. The edges of the V pentomino are: 3,3,2,2,1,1.
   XXX
   X
   X
a(45)=8 because of the following polyomino with edges 5,3,3,1,1,1,1,1.
   XXXXX
   XX
   X

Links

Crossrefs

Cf. A000104, A027709.

Formula

a(4*n+2) = 0.
a(p) = p + (p-1)/2 for any odd prime p.
a(p^2) = p for any prime p.

Extensions

a(33)-a(50) from Sean A. Irvine, Jun 13 2025

A103464 Number of polyominoes consisting of n regular unit heptagons.

Original entry on oeis.org

1, 1, 2, 7, 25, 118, 558, 2876, 14982, 80075, 431889, 2354991, 12930257, 71459124, 396978189, 2215609864
Offset: 3

Views

Author

Sascha Kurz, Jun 09 2006

Keywords

Links

Crossrefs

Cf. A000577, A000104, A000228, A103466, A103467, A103468, A103469, A103470, A103471, A103472, A103473, A120102, A120103, A120104.

A259093 Erroneous version of A006749.

Original entry on oeis.org

0, 0, 0, 1, 9, 19, 84, 316, 1196, 4461, 16750, 62878, 237394, 899265
Offset: 1

Views

Author

Keywords

Comments

Included in accordance with OEIS policy of including erroneous but published sequences to serve as pointers to the correct versions.
a(5) and a(6) are incorrect, but larger terms are all correct.

Links

  • T. R. Parkin, L. J. Lander, and D. R. Parkin, Polyomino Enumeration Results, presented at SIAM Fall Meeting, 1967, and accompanying letter from T. J. Lander (annotated scanned copy). See page 21.
Previous Showing 31-37 of 37 results.

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

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