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A121164
Triangle, real terms extracted from squares of paired terms in arithmetic sequences.
0
-3, -8, -5, -15, -16, -7, -24, -33, -24, -9, -35, -56, -51, -32, -11, -48, -85, -88, -69, -40, -13, -63, -120, -135, -120, -87, -48, -15, -80, -161, -192, -185, -152, -105, -56, -17, -99, -208, -259, -264, -235, -184, -123, -19, -120, -261, -336, -357, -336, -285, -216, -141
OFFSET
1,1
COMMENTS
Left border (-3, -8, -15, -24, ...) unsigned = A013648. Next column (-5, -16, -33, ...) unsigned = A045944.
FORMULA
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.
EXAMPLE
Array of the extracted real terms:
-3, -5, -7, -9, ...
-8, -16, -24, -32, ...
-15, -33, -51, -69, ...
-24, -56, -88, -120, ...
...
Taking antidiagonals we get the triangle:
-3;
-8, -5;
-15, -16, -7;
-24, -33, -24, -9;
-35, -56, -51, -32, -11;
-48, -85, -88, -69, -40, -13;
...
(3,2) = -16 since (taken from the arithmetic sequence 1, 3, 5, ...), (3 + 5i)^2 = (-16 + 30i).
CROSSREFS
Sequence in context: A166492 A120070 A143753 * A086872 A363421 A323760
KEYWORD
sign,tabl
AUTHOR
Gary W. Adamson, Aug 13 2006
STATUS
approved