A121197 Consider the tiling of the plane with squares of two different sizes as in Fig. 2.4.2(g) of Grünbaum and Shephard, p. 74. a(n) is the number of connected figures that can be formed on this tiling, from any n squares.

2, 2, 8, 34, 158, 777, 4006, 21224, 114348, 624222, 3441050, 19121530, 106957272

Offset: 1

Author

N. J. A. Sloane, Aug 17 2006

Keywords

• nonn
• nice
• hard
• more

Comments

The Zucca web site calls these figures "n-DifferentSquares".

Also the number of one-sided polyforms on the faces of the truncated square tiling. - Peter Kagey, May 24 2025

References

• Branko Grünbaum and G. C. Shephard, Tilings and Patterns. W. H. Freeman, New York, 1987.

Links

• Peter Kagey, Illustration of a(5)=158.
• Livio Zucca, PolyMultiForms

Crossrefs

Cf. A121195, A121196, A121198, A343577.

Extensions

More terms from Don Reble, Aug 17 2007

a(13) from Joseph Myers, Oct 06 2011