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A144106
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Eigentriangle, row sums = (2n + 1).
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2
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1, 2, 1, 0, 2, 3, -4, 0, 6, 5, -4, -4, 0, 10, 7, 4, -4, 12, 0, 14, 9, 12, 4, -12, -20, 0, 18, 11, 4, 12, 12, -20, -28, 0, 22, 13, -20, 4, 36, 20, -28, -36, 0, 26, 15, -28, -20, 12, 60, 28, -36, -44, 0, 30, 17
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OFFSET
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0,2
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COMMENTS
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Sum of n-th row terms = rightmost term of next row.
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LINKS
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FORMULA
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Eigentriangle by rows, T(n,k) = A078050(n-k) * X; where X = an infinite lower triangular matrix with (1, 1, 3, 5, 7, 9,...) in the main diagonal and the rest zeros. A078050 is signed: (1, 2, 0, -4, -4, 4, 12, 4, -20, -28,...) = the INVERTi transform of the odd numbers: (1, 3, 5, 7,...).
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EXAMPLE
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First few rows of the triangle =
1;
2, 1;
0, 2, 3;
-4, 0, 6, 5;
-4, -4, 0, 10, 7;
4, -4, -12, 0, 14, 9;
12, 4, -12, -20, 0, 18, 11;
4, 12, 12, -20, -28, 0, 22, 13;
-20, 4, 36, 20, -28, -36, 0, 26, 15;
...
Row 3 = (-4, 0, 6, 5) = (-4*1, 0*1, 3*2, 5*1) = termwise product of (-4, 0, 2, 1) and (1, 1, 3, 5); where (-4, 0, 2, 1) = the first 4 terms of signed A078050 (reversed).
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CROSSREFS
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KEYWORD
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AUTHOR
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STATUS
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approved
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