The OEIS mourns the passing of Jim Simons and is grateful to the Simons Foundation for its support of research in many branches of science, including the OEIS.
login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A354308 Number of free polyjogs with n cells. 0

%I #8 May 24 2022 02:18:45

%S 1,1,4,17,88,503,3071,19372,124575,813020,5361539,35662727,238864272,

%T 1609398564

%N Number of free polyjogs with n cells.

%C A polyjog is a polyform composed of n connected unit squares adjoined along half-edges: every pair of adjacent cells shares an edge of length exactly 1/2. The polyjogs of order n form a subset of polyominoes of order 4n.

%C Figures that differ by a rotation or reflection are considered equivalent.

%C It is not hard to prove that every polyjog can be tiled by unit squares in exactly one way. Therefore, equivalences involving internal rearrangement of unit squares are not relevant (unlike related sequences; cf. A216583).

%H George Sicherman, <a href="http://www.recmath.org/PolyCur/polyjogs/">Catalogue of Polyjogs</a>

%e a(3) = 4, because there are four ways to adjoin three unit squares by half-edges:

%e aa cc cc aa aa

%e aabbcc aa cc aabb aa

%e bb aabb bbcc bb

%e bb cc bbcc

%e cc

%e (In these figures, the three unit squares are depicted by 2 X 2 arrangements of letters a, b, and c.)

%Y Cf. A000105, A216583.

%K nonn,hard,more

%O 1,3

%A _Aaron N. Siegel_, May 23 2022

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified May 28 04:02 EDT 2024. Contains 372900 sequences. (Running on oeis4.)