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A259017 Number of fixed tree polycubes of size n that are proper in n-4 dimensions. 1

%I #22 Sep 08 2022 08:46:13

%S 0,1,172,17041,1382400,104454120,7801139200,593322510704,

%T 46672464052224,3827977546598400,328664453612830720,

%U 29590252898580000000,2794588822832496508928,276747699113763664091136,28712738456619366481920000,3117500646133634877355274240,353783948741967872000000000000

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

%H Colin Barker, <a href="/A259017/b259017.txt">Table of n, a(n) for n = 4..351</a>

%H G. Barequet and M. Shalah, <a href="https://www.youtube.com/watch?v=ojNDm8qKr9A">Automatic Proofs for Formulae Enumerating Proper Polycubes</a>.

%H G. Barequet and M. Shalah, <a href="http://dx.doi.org/10.4230/LIPIcs.SOCG.2015.19">Automatic Proofs for Formulae Enumerating Proper Polycubes</a>.

%F 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.

%o (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

%o (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

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

%K nonn,easy

%O 4,3

%A _Mira Shalah_, Jun 16 2015

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Last modified June 12 12:23 EDT 2024. Contains 373331 sequences. (Running on oeis4.)