A255604 Table read by antidiagonals, T(n,k) is the integer part of the area of a regular k-gon with side length n.
0, 1, 1, 3, 4, 1, 6, 9, 6, 2, 10, 16, 15, 10, 3, 15, 25, 27, 23, 14, 4, 21, 36, 43, 41, 32, 19, 6, 27, 49, 61, 64, 58, 43, 24, 7, 35, 64, 84, 93, 90, 77, 55, 30, 9, 43, 81, 110, 127, 130, 120, 98, 69, 37, 11, 52, 100, 139, 166, 178, 173, 154, 123, 84, 44, 13, 62, 121, 172
Offset: 1
Examples
See table in the links.
Links
- Kival Ngaokrajang, Illustration of T(n,k), n = 1..4, k = 3..6, Example of table
Programs
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Mathematica
t[n_, k_] := Floor[k*n^2/(4 Tan[Pi/k])]; Table[t[n - k + 1, k], {n, 3, 14}, {k, 3 , n}] // Flatten (* to view table: Table[t[n, k], {k, 3, 6}, {n, 6}] // TableForm *) (* Robert G. Wilson v, Feb 28 2015 *) -
PARI
{for(i=1,20,for(n=3,i-1,a=floor(n*(i-n)^2/(4*tan(Pi/n)));print1(a,", ")))}
Formula
T(n,k) = floor(k*n^2/(4*tan(Pi/k))), n >=1, k >=3.
Comments