A056845 Number of distinct connected planar figures that can be formed from n non-overlapping diamonds.

1, 2, 9, 41, 248, 1610, 11065, 78218, 563675, 4113988, 30329616, 225394071, 1686227909

Offset

1,2

Comments

If you look at Vicher's picture of the 40 4-celled polydiamonds (link in A056844), near the middle of the picture is a polydiamond that looks like the traditional 2-D representation of a cube with an extra diamond stuck to the edge. Depending on how you orient the cube, there are actually 2 different ways to form this polydiamond, although there is no change in the perimeter shape. - Larry_Reeves(AT)intranetsolutions.com, Jun 22 2001; edited by Aaron N. Siegel, May 18 2022

Two figures are considered distinct even if their perimeter shapes are identical, provided their internal arrangements of diamonds are distinct (and not related by symmetry). This distinguishes the related sequence A056844 from A056845. The two sequences first diverge at n = 4. - Aaron N. Siegel, May 18 2022

Links

Table of n, a(n) for n=1..13.

M. Keller, More information

M. Vicher, Polyforms

Crossrefs

Cf. A056844, A056785, A056786.

Sequence in context: A192661 A020038 A330016 * A354302 A162273 A289684

Adjacent sequences: A056842 A056843 A056844 * A056846 A056847 A056848

Keyword

nonn,more,hard

Author

James A. Sellers, Aug 28 2000

Extensions

Title clarified, a(6) corrected and a(7)-a(13) from Aaron N. Siegel, May 18 2022

Status

approved