Mira Shalah has authored 4 sequences.
A290868
a(n) is the number of fixed tree polycubes of size n that are proper in n-5 dimensions.
Original entry on oeis.org
0, 1, 568, 116004, 15998985, 1839569920, 194498568156, 19903875199488, 2028587719434848, 209368404017676288, 22100537701746000000, 2400300773277150740480, 269182253907724040230656, 31234215889947671471849472, 3753858472917234012947022848, 467486957946431078400000000000
Offset: 5
- 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.
A290738 gives the total number of fixed n-cell polycubes (not necessarily trees) that are proper in n-5 dimensions.
A290738
a(n) is the number of fixed polycubes of size n that are proper in n-5 dimensions.
Original entry on oeis.org
0, 1, 758, 154741, 20762073, 2323972976, 240154383596, 24109617950208, 2417940914461280, 246158020396388352, 25680108955640400000, 2760762217507260989440, 306854769192894226859776, 35326258772832011339956224, 4216066596599500902861091840, 521775392548443914240000000000
Offset: 5
- 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.
A259015 gives the number of n-cell polycubes that are proper in n-4 dimensions.
A259017
Number of fixed tree polycubes of size n that are proper in n-4 dimensions.
Original entry on oeis.org
0, 1, 172, 17041, 1382400, 104454120, 7801139200, 593322510704, 46672464052224, 3827977546598400, 328664453612830720, 29590252898580000000, 2794588822832496508928, 276747699113763664091136, 28712738456619366481920000, 3117500646133634877355274240, 353783948741967872000000000000
Offset: 4
A259015 gives the total number of fixed polycubes (not necessarily trees) proper in n-4 dimensions.
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[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
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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
A259015
The number of fixed polycubes of size n that span n-4 dimensions.
Original entry on oeis.org
0, 1, 214, 21225, 1688424, 125055400, 9178531200, 687848686448, 53435249786880, 4336107249936384, 368887991492608000, 32948013484980000000, 3090086319932923969536, 304136142049322287011840, 31382704663810285705887744, 3390841628447041935421747200, 383124440688361472000000000000
Offset: 4
- G. Barequet, M. Shalah, Automatic Proofs for Formulae Enumerating Proper Polycubes, 31st International Symposium on Computational Geometry (SoCG’15). Editors: Lars Arge and János Pach; pp. 19-22, 2015.
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[2^(n-7)*n^(n-9)*(n-4)*(8*n^8-128*n^7+828*n^6-2930*n^5 +7404*n^4-17523*n^3+41527*n^2-114302*n+204960)/6: n in [4..20]]; // Vincenzo Librandi, Jun 20 2015
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Table[2^(n - 7) n^(n - 9) (n - 4) (8 n^8 - 128 n^7 + 828 n^6 - 2930 n^5 + 7404 n^4 - 17523 n^3 + 41527 n^2 - 114302 n + 204960)/6, {n, 4, 20}] (* Michael De Vlieger, Jun 19 2015 *)
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a(n)=2^(n-7)*n^(n-9)*(n-4)*(8*n^8-128*n^7+828*n^6 -2930*n^5 +7404*n^4-17523*n^3 +41527*n^2-114302*n +204960)/6 \\ Charles R Greathouse IV, Jun 16 2015
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