A259017 Number of fixed tree polycubes of size n that are proper in n-4 dimensions.

0, 1, 172, 17041, 1382400, 104454120, 7801139200, 593322510704, 46672464052224, 3827977546598400, 328664453612830720, 29590252898580000000, 2794588822832496508928, 276747699113763664091136, 28712738456619366481920000, 3117500646133634877355274240, 353783948741967872000000000000

Offset: 4

Author

Mira Shalah, Jun 16 2015

Keywords

• nonn
• easy

Links

• Colin Barker, Table of n, a(n) for n = 4..351
• G. Barequet and M. Shalah, Automatic Proofs for Formulae Enumerating Proper Polycubes.
• G. Barequet and M. Shalah, Automatic Proofs for Formulae Enumerating Proper Polycubes.

Crossrefs

A259015 gives the total number of fixed polycubes (not necessarily trees) proper in n-4 dimensions.

Programs

Magma

[2^(n-7)*n^(n-9)*(n-4)*(8*n^8 - 140*n^7 + 1010*n^6 - 3913*n^5 + 9201*n^4 - 15662*n^3 + 34500*n^2 - 120552*n + 221760)/6: n in [4..20]]; // Vincenzo Librandi, Jun 20 2015

PARI

a(n) = 2^(n-7) * n^(n-9) * (n-4) * (8*n^8-140*n^7+1010*n^6 -3913*n^5 +9201*n^4-15662*n^3+34500*n^2-120552*n +221760)/6 \\ Colin Barker, Jun 16 2015

Formula

a(n) = 2^(n-7)*n^(n-9)*(n-4)*(8*n^8 - 140*n^7 + 1010*n^6 - 3913*n^5 + 9201*n^4 - 15662*n^3 + 34500*n^2 - 120552*n + 221760)/6.