A216492 Number of inequivalent connected planar figures that can be formed from n 1 X 2 rectangles (or dominoes) such that each pair of touching rectangles shares exactly one edge, of length 1, and the adjacency graph of the rectangles is a tree.

1, 1, 3, 18, 139, 1286, 12715, 130875

Offset

0,3

Comments

Figures that differ only by a rotation and/or reflection are regarded as equivalent (cf. A216581).

A216583 is A216492 without the condition that the adjacency graph of the dominoes forms a tree.

This is a subset of polydominoes. It appears that a(n) < A216583(n) < A056785(n) < A056786(n) < A210996(n) < A210988(n) < A210986(n), if n >= 3. - Omar E. Pol, Sep 15 2012

Links

Table of n, a(n) for n=0..7.

C. E. Lozada, Illustration of initial terms: planar figures with up to 3 dominoes

N. J. A. Sloane, Illustration of initial terms of A056786, A216598, A216583, A216595, A216492, A216581 (Exclude figures marked (A) or (B))

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

Example

One domino (2 X 1 rectangle) is placed on a table.
A 2nd domino is placed touching the first only in a single edge (length 1). The number of different planar figures is a(2)=3.
A 3rd domino is placed in any of the last figures, touching it and sharing just a single edge with it. The number of different planar figures is a(3)=18.
When n=4, we might place 4 dominoes in a ring, with a free square in the center. This is however not allowed, since the adjacency graph is a cycle, not a tree.

Crossrefs

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

Without the condition that the adjacency graph forms a tree we get A216583 and A216595.

If we allow two long edges to meet we get A056786 and A216598.

Sequence in context: A357403 A039618 A183363 * A127129 A186266 A260506

Adjacent sequences: A216489 A216490 A216491 * A216493 A216494 A216495

Keyword

nonn,more,nice

Author

César Eliud Lozada, Sep 07 2012

Extensions

Edited by N. J. A. Sloane, Sep 09 2012

Status

approved