A364922 a(n) is the square of the side length of a simplex whose n-dimensional inner hypervolume is equal to its (n-1)-dimensional surface hypervolume. As a result, the sequence starts at n=2.
48, 216, 640, 1500, 3024, 5488, 9216, 14580, 22000, 31944, 44928, 61516, 82320, 108000, 139264, 176868, 221616, 274360, 336000, 407484, 489808, 584016, 691200, 812500, 949104, 1102248, 1273216, 1463340, 1674000, 1906624, 2162688, 2443716, 2751280, 3087000
Offset: 2
Links
- Harvey P. Dale, Table of n, a(n) for n = 2..1000
- Index entries for linear recurrences with constant coefficients, signature (5,-10,10,-5,1).
Programs
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Mathematica
Table[2*n^3*(n + 1), {n, 2, 50}] (* Paolo Xausa, Apr 18 2024 *) LinearRecurrence[{5,-10,10,-5,1},{48,216,640,1500,3024},40] (* Harvey P. Dale, Aug 27 2024 *) -
Python
def a(n): return 2 * n**3 * (n + 1) print([a(n) for n in range(2, 50)])
Formula
a(n) = 2*n^3*(n+1) = 2*A179824(n+1).
From Stefano Spezia, Apr 13 2024: (Start)
G.f.: 4*x^2*(12 - 6*x + 10*x^2 - 5*x^3 + x^4)/(1 - x)^5.
a(n) = 4*A019582(n+1). (End)
Comments