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Search: id:A121164
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| A121164 |
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Triangle, real terms extracted from squares of paired terms in arithmetic sequences. |
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+0
1
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| -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
(list; table; graph; listen)
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OFFSET
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1,1
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COMMENT
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Left border (-3, -8, -15, -24...) unsigned = A013648. Next column (-5, -16, -33...) unsigned = A045944
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FORMULA
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Form an array of the arithemetic 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.
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EXAMPLE
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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).
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CROSSREFS
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Cf. A013648, A045944.
Sequence in context: A050093 A120072 A120070 this_sequence A086872 A054792 A090347
Adjacent sequences: A121161 A121162 A121163 this_sequence A121165 A121166 A121167
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KEYWORD
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sign,tabl
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AUTHOR
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Gary W. Adamson (qntmpkt(AT)yahoo.com), Aug 13 2006
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