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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A245660 Number of unitary polyominoes without holes with n cells. A unitary polyomino is a polyomino whose edges all have length 1.

Original entry on oeis.org

1, 0, 0, 0, 1, 0, 0, 1, 1, 0, 2, 1, 2, 4, 5, 4, 12, 13, 20, 29, 52, 67, 106, 173, 269, 375, 658, 991, 1512, 2425, 3896, 5902, 9454, 15146, 23601, 37050, 59908, 93777, 148151, 237228, 375893, 593773, 948623, 1508823, 2393035, 3812023, 6083290, 9666024, 15404085, 24592209
Offset: 1

Views

Author

Joerg Arndt, Jul 28 2014

Keywords

Links

Crossrefs

Cf. A245620, number of unitary polyominoes with n cells.

Extensions

Added a(16)-a(20), George Sicherman, Jul 29 2014
a(21)-a(43) from John Mason, Apr 21 2023
a(44)-a(50) from John Mason, Apr 26 2023

A330442 The number of free polyominoes with n cells which, when drawn on a 2D square grid, contain an Eulerian path.

Original entry on oeis.org

1, 1, 1, 2, 3, 6, 8, 18
Offset: 1

Views

Author

Scott R. Shannon, Dec 14 2019

Keywords

Comments

a(n) is the total number of free polyominoes containing n cells which, when drawn on a 2D square grid, contain an Eulerian path. Such polyominoes must have all edges of length one, see A245620, have one or two edges of length two with all other edges of length one, or else have one edge of length three with all other edges of length one. These edges also include those bordering internal holes.

Examples

			The one 3-cell polyomino:
  +---+---+
  |   |   |
  +---+---+
      |   |
      +---+
The two 4-cell polyominoes:
  +---+---+---+    +---+---+
  |   |   |   |    |   |   |
  +---+---+---+    +---+---+---+
      |   |            |   |   |
      +---+            +---+---+
The three 5-cell polyominoes:
  +---+---+            +---+        +---+---+
  |   |   |            |   |        |   |   |
  +---+---+---+    +---+---+---+    +---+---+---+
      |   |   |    |   |   |   |        |   |   |
      +---+---+    +---+---+---+        +---+---+
      |   |            |   |                |   |
      +---+            +---+                +---+

Links

Crossrefs

Cf. A000105, A268311, A245620.
Showing 1-2 of 2 results.

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