A255604 - OEIS

%I #20 Jan 09 2025 02:17:33

%S 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,

%T 6,27,49,61,64,58,43,24,7,35,64,84,93,90,77,55,30,9,43,81,110,127,130,

%U 120,98,69,37,11,52,100,139,166,178,173,154,123,84,44,13,62,121,172

%N Table read by antidiagonals, T(n,k) is the integer part of the area of a regular k-gon with side length n.

%C See illustration in the links.

%H Kival Ngaokrajang, <a href="/A255604/a255604_2.pdf">Illustration of T(n,k), n = 1..4, k = 3..6</a>, <a href="/A255604/a255604_1.pdf">Example of table</a>

%F T(n,k) = floor(k*n^2/(4*tan(Pi/k))), n >=1, k >=3.

%e See table in the links.

%t t[n_, k_] := Floor[k*n^2/(4 Tan[Pi/k])]; Table[t[n - k + 1, k], {n, 3, 14}, {k, 3 , n}] // Flatten

%t (* to view table: Table[t[n, k], {k, 3, 6}, {n, 6}] // TableForm *) (* _Robert G. Wilson v_, Feb 28 2015 *)

%o (PARI){for(i=1,20,for(n=3,i-1,a=floor(n*(i-n)^2/(4*tan(Pi/n)));print1(a,", ")))}

%Y Row 1: A011865.

%Y Columns 1,2,3,4,10: A171971, A000290, A255605, A255606, A172526.

%K nonn,tabl

%O 1,4

%A _Kival Ngaokrajang_, Feb 27 2015