A210996 Number of free polyominoes with 2n cells.

1, 1, 5, 35, 369, 4655, 63600, 901971, 13079255, 192622052, 2870671950, 43191857688, 654999700403, 9999088822075, 153511100594603, 2368347037571252, 36695016991712879, 570694242129491412, 8905339105809603405, 139377733711832678648, 2187263896664830239467, 34408176607279501779592

Offset

0,3

Comments

It appears that we can write A216492(n) < A216583(n) < A056785(n) < A056786(n) < a(n) < A210988(n) < A210986(n), if n >= 3. - Omar E. Pol, Sep 16 2012

Links

John Mason, Table of n, a(n) for n = 0..25

Herman Tulleken, Polyominoes 2.2: How they fit together, (2019).

Eric Weisstein's World of Mathematics, Polyomino

Wikipedia, All 5 free tetrominoes, Illustration of a(2) = 5.

Wikipedia, All 35 free hexominoes, Illustration of a(3) = 35.

Wikipedia, All 369 free octominoes, Illustration of a(4) = 369.

Wikipedia, Polyomino

Formula

a(n) = A000105(2n).

a(n) = A213376(n) + A056785(n). - R. J. Mathar, Feb 08 2023

Example

For n = 1 there is only one free domino. For n = 2 there are 5 free tetrominoes. For n = 3 there are 35 free hexominoes. For n = 4 there are 369 free octominoes (see link section).

Mathematica

A000105 = Cases[Import["https://oeis.org/A000105/b000105.txt", "Table"], {_, _}][[All, 2]];
Partition[A000105, 2][[All, 1]] (* Jean-François Alcover, Jan 03 2020 *)

Crossrefs

Bisection of A000105.

Cf. A000988, A056785, A056786, A210988, A210997, A216492, A216583.

Sequence in context: A258902 A371028 A125864 * A204290 A059865 A247596

Adjacent sequences: A210993 A210994 A210995 * A210997 A210998 A210999

Keyword

nonn

Author

Omar E. Pol, Sep 15 2012

Extensions

More terms from John Mason, Apr 15 2023

Status

approved