A057103 Triangle of congrua: T(n,k) = 4*n*k(n^2-k^2) with n>k>0 and starting at T(2,1) = 24. A055096(n)^2 + a(n) is a square, as is A055096(n)^2 - a(n).

24, 96, 120, 240, 384, 336, 480, 840, 960, 720, 840, 1536, 1944, 1920, 1320, 1344, 2520, 3360, 3696, 3360, 2184, 2016, 3840, 5280, 6144, 6240, 5376, 3360, 2880, 5544, 7776, 9360, 10080, 9720, 8064, 4896, 3960, 7680, 10920, 13440, 15000, 15360, 14280, 11520, 6840

Offset: 2

Author

Henry Bottomley, Aug 02 2000

Keywords

• nonn
• tabl

Comments

Refers to A057102, which had an incorrect description and has been replaced by A256418. As a result the present sequence should be re-checked. - N. J. A. Sloane, Apr 06 2015

Examples

			T(2,1) = 4*2*1*(4-1) = 5^2-1^2 = 7^2-5^2 = 24.
Triangle begins:
   24;
   96,  120;
  240,  384,  336;
  480,  840,  960,  720;
  840, 1536, 1944, 1920, 1320;
  ...
		

Links

• Eric Weisstein's World of Mathematics, Congruum Problem.

Crossrefs

Cf. possible congrua A057102. See also A055096.

Programs

Mathematica

T[n_, k_] := 4 n k (n^2 - k^2);
Table[T[n, k], {n, 2, 10}, {k, 1, n - 1}] // Flatten (* Jean-François Alcover, Feb 25 2019 *)

Extensions

Offset corrected by Alois P. Heinz, Feb 25 2019