login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo

Thanks to everyone who made a donation during our annual appeal!
To see the list of donors, or make a donation, see the OEIS Foundation home page.

Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A118356 Number of clusters with n vertices, n-1 edges and zero contacts on the simple cubic lattice. 7
1, 3, 15, 83, 486, 2967, 18748, 121725, 807381, 5447203, 37264974, 257896500, 1802312605, 12701190885, 90157130289, 644022007040, 4626159163233 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

a(n)<=A001931(n) due to the "no-contact" restriction.

An alternative wording for a(n) is the number of n-cell fixed tree-like polycubes in 3 dimensions. - Gill Barequet, May 25 2011

REFERENCES

G. Aleksandrowicz and G. Barequet, Parallel enumeration of lattice animals, Proc. 5th Int. Frontiers of Algorithmics Workshop, Zhejiang, China, Lecture Notes in Computer Science, 6681, Springer-Verlag, 90-99, May 2011.

LINKS

Table of n, a(n) for n=1..17.

N. Madras, C. E. Soteros, S. G. Whittington, J. L. Martin et al., The free energy of a collapsing branched polymer, J Phys A: Math Gen 23 (1990) 5327-5350

CROSSREFS

Cf. A066158 (fixed tree-like polyominoes), A191094 - A191098 (fixed tree-like polycubes in 4, 5, 6, 7, and 8 dimensions, resp.)

Sequence in context: A213096 A052451 A026019 * A074552 A193658 A195885

Adjacent sequences:  A118353 A118354 A118355 * A118357 A118358 A118359

KEYWORD

nonn,more

AUTHOR

R. J. Mathar, May 14 2006

EXTENSIONS

a(1)=1 added by Gill Barequet, May 25 2011

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified January 22 13:41 EST 2020. Contains 331149 sequences. (Running on oeis4.)