A216583 Number of unit-conjoined polydominoes of order n.

1, 1, 3, 20, 171, 1733, 18962, 215522, 2507188, 29635101

Offset: 0

Author

N. J. A. Sloane, Sep 09 2012

Keywords

• nonn
• more
• hard

Comments

A unit-conjoined polydomino is formed from n 1 X 2 non-overlapping rectangles (or dominoes) such that each pair of touching rectangles shares an edge of length 1. The internal arrangement of dominoes is not significant: figures are counted as distinct only if the shapes of their perimeters are different.

Figures that differ only by a rotation and/or reflection are regarded as equivalent (cf. A216595).

This sequence is A216492 without the condition that the adjacency graph of the dominoes forms a tree.

This is a subset of polydominoes. It appears that A216492(n) < a(n) < A056785(n) < A056786(n) < A210996(n) < A210988(n) < A210986(n), if n >= 3. - Omar E. Pol, Sep 17 2012

Links

• César E. Lozada, Illustration of terms n <= 4 of A216583
• N. J. A. Sloane, Illustration of initial terms of A056786, A216598, A216583, A216595, A216492, A216581 (Exclude figures marked (A))
• N. J. A. Sloane, Illustration of third term of A056786, A216598, A216583, A216595, A216492, A216581 (a better drawing for the third term)
• M. Vicher, Polyforms
• Index entries for sequences related to dominoes

Crossrefs

Cf. A056786, A216598, A216583, A216595, A216492, A216581.

Extensions

a(4)-a(6) added by César Eliud Lozada, Sep 09 2012

a(7)-a(9) and name edited by Aaron N. Siegel, May 18 2022