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Triangle of numbers (when unsigned) related to congruum problem: T(n,k)=k^2+2nk-n^2 with n>k>0 and starting at T(2,1)=1.
2

%I #7 Apr 06 2015 10:47:00

%S 1,-2,7,-7,4,17,-14,-1,14,31,-23,-8,9,28,49,-34,-17,2,23,46,71,-47,

%T -28,-7,16,41,68,97,-62,-41,-18,7,34,63,94,127,-79,-56,-31,-4,25,56,

%U 89,124,161,-98,-73,-46,-17,14,47,82,119,158,199,-119,-92,-63,-32,1,36,73,112,153,196,241,-142,-113,-82,-49,-14,23,62,103

%N Triangle of numbers (when unsigned) related to congruum problem: T(n,k)=k^2+2nk-n^2 with n>k>0 and starting at T(2,1)=1.

%C Signed values are only relevant for the explicit formula.

%C Refers to A057102, which had an incorrect description and has been replaced by A256418.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 Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/CongruumProblem.html">Congruum Problem.</a>

%F Unsigned: a(n) =sqrt(A055096(n)^2-A057103(n)) =sqrt(A056203(n)^2-2*A057103(n)).

%e a(1)=T(2,1)=1^2+2*2*1-2^2=1

%Y Cf. A057102. The congruum problem is about finding solutions for h (A057103) where there are integers x (A055096), y (A057105 unsigned) and z (A056203) such that h=x^2-y^2=z^2-x^2.

%K sign,tabl

%O 1,2

%A _Henry Bottomley_, Aug 02 2000