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.

User: P. Christopher Staecker

P. Christopher Staecker's wiki page.

P. Christopher Staecker has authored 6 sequences.

A306725 Number of connected strong irreducible digital images of n points up to strong homotopy equivalence.

Original entry on oeis.org

1, 0, 0, 1, 2, 9, 46, 507, 11800
Offset: 1

Views

Author

P. Christopher Staecker, Mar 06 2019

Keywords

Comments

"Strong irreducible" means not strong homotopy equivalent to an image of fewer points. Each term is greater than or equal to the corresponding term of A248571.

Links

Crossrefs

Cf. A248571.

A255540 Number of connected digital images in Z^2 (regarding each point as connected to its 8 neighbors) on n points up to isomorphism.

Original entry on oeis.org

1, 1, 2, 6, 15, 51, 173, 681, 2682
Offset: 1

Views

Author

P. Christopher Staecker, Feb 24 2015

Keywords

Comments

Also the number of polyplets (A030222) on n points up to isomorphism of adjacency graphs.

Examples

			For n=4 the a(4)=6 images are:
X   X X    X    XX    X     X
X    X    X X   XX   XX   XX
X    X     X         X     X
X

Links

Crossrefs

Cf. A255539.

A255538 Number of connected rigid digital images of n points, up to isomorphism.

Original entry on oeis.org

1, 0, 0, 0, 0, 0, 2, 26, 544
Offset: 1

Views

Author

P. Christopher Staecker, Feb 24 2015

Keywords

Comments

Rigid means that the identity map is not homotopic to any other map.

Links

Crossrefs

Cf. A248571, A255537.

A255539 Number of digital images in Z^2 with 4-adjacency on n points up to isomorphism.

Original entry on oeis.org

1, 1, 1, 3, 4, 10, 19, 51, 112, 300, 746, 2042, 5450, 15197, 42192, 119561, 339594
Offset: 1

Views

Author

P. Christopher Staecker, Feb 24 2015

Keywords

Comments

Also the number of polyominoes on n points, up to isomorphism of the adjacency graph.
Also the number of "grid graphs" (finite induced subgraphs of the integer lattice using only horizontal and vertical edges) on n vertices.

Examples

			a(4) = 3: (1) the square tetromino has the 4-cycle as its "adjacency graph"; (2) the T-tetromino corresponds to the claw graph; (3) the straight, skew, and L-tetromino all correspond to the 4-path.

Links

Crossrefs

Cf. A000105, A181528, A255540.

Extensions

a(13)-a(16) from Giovanni Resta, Apr 10 2020
a(17) from Tang et al. added by Andrey Zabolotskiy, Oct 23 2022

A255537 Number of connected pointed-irreducible digital images of n points up to homotopy equivalence.

Original entry on oeis.org

1, 0, 0, 0, 1, 2, 9, 68, 1110
Offset: 1

Views

Author

P. Christopher Staecker, Feb 24 2015

Keywords

Comments

"Pointed-irreducible" means that the identity map is not homotopic to any nonsurjective map having a fixed point.

Links

Crossrefs

Cf. A248571.

A248571 Number of connected irreducible digital images of n points up to homotopy equivalence.

Original entry on oeis.org

1, 0, 0, 0, 1, 1, 3, 28, 547
Offset: 1

Views

Author

P. Christopher Staecker, Oct 13 2014

Keywords

Comments

"Irreducible" means not homotopy equivalent to any digital image of fewer points. The terms are nonzero for all n>4, and are believed to be strictly increasing for n>6.

Links

Extensions

a(8)-a(9) from P. Christopher Staecker, Feb 24 2015

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