A089083 T(n,k) = (floor(k*n/2) * ceiling(k*n/2))^2, triangular array read by rows, 1 <= k <= n.

0, 1, 16, 4, 81, 400, 16, 256, 1296, 4096, 36, 625, 3136, 10000, 24336, 81, 1296, 6561, 20736, 50625, 104976, 144, 2401, 12100, 38416, 93636, 194481, 360000, 256, 4096, 20736, 65536, 160000, 331776, 614656, 1048576, 400, 6561, 33124, 104976, 256036, 531441, 984064, 1679616, 2689600

Offset

1,3

Links

Michael De Vlieger, Table of n, a(n) for n = 1..11325, rows 1 <= n <= 150, flattened.

Formula

T(n,1) = A002620(n)^2;

T(n,2) = A000290(n)^2 for n > 1;

T(n,4) = A016742(n)^2 for n > 3.

Example

Triangle begins:
   0
   1    16
   4    81   400
  16   256  1296   4096
  36   625  3136  10000  24336
  ...

Mathematica

T[n_, k_] := Floor[k n/2]^2 * Ceiling[k n/2]^2;
Table[T[n, k], {n, 1, 10}, {k, 1, n}] // Flatten (* Jean-François Alcover, Nov 16 2021 *)

Crossrefs

Sequence in context: A040247 A245826 A331222 * A363191 A102411 A336782

Adjacent sequences: A089080 A089081 A089082 * A089084 A089085 A089086

Keyword

nonn,tabl

Author

Reinhard Zumkeller, Dec 04 2003

Extensions

Name and formulas corrected by Jean-François Alcover, Nov 16 2021

Status

approved