A290868 a(n) is the number of fixed tree polycubes of size n that are proper in n-5 dimensions.

0, 1, 568, 116004, 15998985, 1839569920, 194498568156, 19903875199488, 2028587719434848, 209368404017676288, 22100537701746000000, 2400300773277150740480, 269182253907724040230656, 31234215889947671471849472, 3753858472917234012947022848, 467486957946431078400000000000

Offset: 5

Author

Mira Shalah, Aug 12 2017

Keywords

• nonn

Comments

Denoted DT(n,n-5).

Links

• G. Barequet and M. Shalah, Counting n-cell polycubes proper in n-k dimensions, European Journal of Combinatorics, 63 (2017), 146-163.
• G. Barequet and M. Shalah, Automatic Proofs for Formulae Enumerating Proper Polycubes, In Proceedings of the 8th European Conference on Combinatorics, Graph Theory and Applications, 49 (2015), 145-151, 2015.
• G. Barequet and M. Shalah, Automatic Proofs for Formulae Enumerating Proper Polycubes, In Video Review at the 31st Symposium on Computational Geometry, 19-22, 2015.
• M. Shalah, Automatic Proofs for Formulae Enumerating Proper Polycubes, Youtube, 2015.

Crossrefs

A290738 gives the total number of fixed n-cell polycubes (not necessarily trees) that are proper in n-5 dimensions.

Formula

a(n) = 2^(n-9)*n^(n-11)*(n-5)*(240*n^11 - 6480*n^10 + 73640*n^9 - 461232*n^8 + 1778615*n^7 - 4707195*n^6 + 11632070*n^5 - 41919528*n^4 + 158857920*n^3 - 483329520*n^2 + 1481660640*n - 2863123200)/360. (proved)