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%I #8 Feb 13 2022 23:36:10
%S -3,-8,-5,-15,-16,-7,-24,-33,-24,-9,-35,-56,-51,-32,-11,-48,-85,-88,
%T -69,-40,-13,-63,-120,-135,-120,-87,-48,-15,-80,-161,-192,-185,-152,
%U -105,-56,-17,-99,-208,-259,-264,-235,-184,-123,-19,-120,-261,-336,-357,-336,-285,-216,-141
%N Triangle, real terms extracted from squares of paired terms in arithmetic sequences.
%C Left border (-3, -8, -15, -24, ...) unsigned = A013648. Next column (-5, -16, -33, ...) unsigned = A045944.
%F Form an array of the arithmetic sequences: (1, 2, 3, ...); (1, 3, 5, ...); (1, 4, 7, ...); and consider each pair as a complex term; e.g., (1 + 2i), (2 + 3i), then square each complex term and extract the real integer. Antidiagonals become rows of the triangle.
%e Array of the extracted real terms:
%e -3, -5, -7, -9, ...
%e -8, -16, -24, -32, ...
%e -15, -33, -51, -69, ...
%e -24, -56, -88, -120, ...
%e ...
%e Taking antidiagonals we get the triangle:
%e -3;
%e -8, -5;
%e -15, -16, -7;
%e -24, -33, -24, -9;
%e -35, -56, -51, -32, -11;
%e -48, -85, -88, -69, -40, -13;
%e ...
%e (3,2) = -16 since (taken from the arithmetic sequence 1, 3, 5, ...), (3 + 5i)^2 = (-16 + 30i).
%Y Cf. A013648, A045944.
%K sign,tabl
%O 1,1
%A _Gary W. Adamson_, Aug 13 2006
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