A290868 - OEIS

%I #25 Aug 18 2017 18:17:32

%S 0,1,568,116004,15998985,1839569920,194498568156,19903875199488,

%T 2028587719434848,209368404017676288,22100537701746000000,

%U 2400300773277150740480,269182253907724040230656,31234215889947671471849472,3753858472917234012947022848,467486957946431078400000000000

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

%C Denoted DT(n,n-5).

%H G. Barequet and M. Shalah, <a href="https://doi.org/10.1016/j.ejc.2017.03.006">Counting n-cell polycubes proper in n-k dimensions</a>, European Journal of Combinatorics, 63 (2017), 146-163.

%H G. Barequet and M. Shalah, <a href="https://doi.org/10.1016/j.endm.2015.06.022">Automatic Proofs for Formulae Enumerating Proper Polycubes</a>, In Proceedings of the 8th European Conference on Combinatorics, Graph Theory and Applications, 49 (2015), 145-151, 2015.

%H G. Barequet and M. Shalah, <a href="http://drops.dagstuhl.de/opus/volltexte/2015/5088/pdf/5.pdf">Automatic Proofs for Formulae Enumerating Proper Polycubes</a>, In Video Review at the 31st Symposium on Computational Geometry, 19-22, 2015.

%H M. Shalah, <a href="https://youtu.be/ojNDm8qKr9A">Automatic Proofs for Formulae Enumerating Proper Polycubes</a>, Youtube, 2015.

%F 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)

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

%K nonn

%O 5,3

%A _Mira Shalah_, Aug 12 2017