A101145 List of molecules in Hintze-Adami artificial chemistry (see comments for definition).

11, 22, 33, 121, 132, 231, 1221, 1232, 1331, 2321, 2332, 12221, 12232, 12331, 13321, 13332, 23221, 23232, 23331, 122221, 122232, 122331, 123321, 123332, 133221, 133232, 133331, 232221, 232232, 232331, 233321, 233332, 1222221, 1222232

Offset

0,1

Comments

These molecules are composed of three types of atoms called 1, 2 and 3. The atoms are arranged linearly. Each atom shares bonds with the adjacent atoms. Each atom must carry as many bonds as the numeral representing it.

The members of this sequence are arranged in numerical order.

The reference states that the molecules "are numbered according to their complexity (length and type of atoms)", which is ambiguous.

For n > 2 there are fibonacci(n+1) members of length n.

Hintze and Adami arbitrarily chose a maximum length of 12, resulting in 608 total members; the last is 233333333332.

All terms are divisible by 11.

Links

Table of n, a(n) for n=0..33.

Arend Hintze and Christoph Adami, Evolution of complex modular biological networks. Page 3 defines the set of valid molecules; p. 17 lists a(0) through a(5) and a(607).

Example

Using "-" to represent single bonds and "=" to represent double bonds, some members are a(0) = 1-1, a(4) = 2=3-1 and a(607) = 2=3-3=3-3=3-3=3-3=3-3=2.
2222 is not a member because the first 2 must share two bonds with the second 2, so the second 2 has no bonds left to share with the third 2.

Crossrefs

Cf. A000045.

Sequence in context: A273992 A283927 A239018 * A109016 A084025 A061157

Adjacent sequences: A101142 A101143 A101144 * A101146 A101147 A101148

Keyword

base,easy,fini,nonn

Author

Jonathan Vos Post, Jun 03 2007

Extensions

Edited and extended by David Wasserman, Mar 05 2008

Status

approved