A255604 Table read by antidiagonals, T(n,k) is 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

1,4

Comments

See illustration in the links.

Links

Table of n, a(n) for n=1..69.

Kival Ngaokrajang, Illustration of T(n,k), n = 1..4, k = 3..6, Example of table

Formula

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

Example

See table in the links.

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 *)

Prog

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

Crossrefs

Row 1: A011865.

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

Sequence in context: A286577 A175323 A359268 * A132700 A193794 A281862

Adjacent sequences: A255601 A255602 A255603 * A255605 A255606 A255607

Keyword

nonn,tabl

Author

Kival Ngaokrajang, Feb 27 2015

Status

approved