A387286 Number of 2 X 2 square tiles in a discrete 4-dimensional hypercube of side length n.
0, 16, 132, 504, 1360, 3000, 5796, 10192, 16704, 25920, 38500, 55176, 76752, 104104, 138180, 180000, 230656, 291312, 363204, 447640, 546000, 659736, 790372, 939504, 1108800, 1300000, 1514916, 1755432, 2023504, 2321160, 2650500, 3013696, 3412992, 3850704, 4329220, 4851000, 5418576, 6034552, 6701604, 7422480
Offset: 1
Examples
a(2) = 16, a(3) = 132, a(4) = 504
Links
- Salvatore Ferraro, Number of tiles in a discrete 4D hypercube, Zenodo, 2025.
- Index entries for linear recurrences with constant coefficients, signature (5,-10,10,-5,1).
Programs
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Maple
a := n -> (n-1)^2*(3*n^2 + 2*n): seq(a(n), n=1..40);
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Mathematica
a[n_] := (n - 1)^2*(3 n^2 + 2 n); Table[a[n], {n, 1, 40}] -
Python
def a(n): return (n - 1)**2 * (3*n**2 + 2*n) print([a(n) for n in range(1, 41)])
Formula
a(n) = (n - 1)^2 * (3*n^2 + 2*n) = 3*n^4 - 4*n^3 - n^2 + 2*n.
G.f.: 4*x^3*(4 + 13*x + x^2)/(1 - x)^5. - Stefano Spezia, Aug 25 2025
Comments