A290738 a(n) is the number of fixed polycubes of size n that are proper in n-5 dimensions.

0, 1, 758, 154741, 20762073, 2323972976, 240154383596, 24109617950208, 2417940914461280, 246158020396388352, 25680108955640400000, 2760762217507260989440, 306854769192894226859776, 35326258772832011339956224, 4216066596599500902861091840, 521775392548443914240000000000

Offset: 5

Author

Mira Shalah, Aug 12 2017

Keywords

• nonn

Comments

Denoted DX(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

A259015 gives the number of n-cell polycubes that are proper in n-4 dimensions.

Diagonal 5 of A195739.

Formula

a(n) = 2^(n-12)*n^(n-11)*(n-5)*(240*n^11 - 6000*n^10 + 62240*n^9 - 356232*n^8 + 1335320*n^7 - 4062240*n^6 + 12397445*n^5 - 42322743*n^4 + 150403080*n^3 - 535510740*n^2 + 1923269040*n - 3731495040)/45. (proved)