A216583 Number of unit-conjoined polydominoes of order n.

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

Offset

0,3

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

Table of n, a(n) for n=0..9.

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.

Sequence in context: A051643 A213377 A357094 * A354018 A154644 A321276

Adjacent sequences: A216580 A216581 A216582 * A216584 A216585 A216586

Keyword

nonn,more,hard

Author

N. J. A. Sloane, Sep 09 2012

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

Status

approved