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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).

%I A057103 #16 Feb 16 2025 08:32:43
%S A057103 24,96,120,240,384,336,480,840,960,720,840,1536,1944,1920,1320,1344,
%T A057103 2520,3360,3696,3360,2184,2016,3840,5280,6144,6240,5376,3360,2880,
%U A057103 5544,7776,9360,10080,9720,8064,4896,3960,7680,10920,13440,15000,15360,14280,11520,6840
%N 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).
%C A057103 Refers to A057102, which had an incorrect description and has been replaced by A256418.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
%H A057103 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/CongruumProblem.html">Congruum Problem.</a>
%e A057103 T(2,1) = 4*2*1*(4-1) = 5^2-1^2 = 7^2-5^2 = 24.
%e A057103 Triangle begins:
%e A057103    24;
%e A057103    96,  120;
%e A057103   240,  384,  336;
%e A057103   480,  840,  960,  720;
%e A057103   840, 1536, 1944, 1920, 1320;
%e A057103   ...
%t A057103 T[n_, k_] := 4 n k (n^2 - k^2);
%t A057103 Table[T[n, k], {n, 2, 10}, {k, 1, n - 1}] // Flatten (* _Jean-François Alcover_, Feb 25 2019 *)
%Y A057103 Cf. possible congrua A057102. See also A055096.
%K A057103 nonn,tabl
%O A057103 2,1
%A A057103 _Henry Bottomley_, Aug 02 2000
%E A057103 Offset corrected by _Alois P. Heinz_, Feb 25 2019