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A145462
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Eigentriangle, row sums = the Padovan sequence, A000931
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1
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1, 1, 1, -1, 1, 2, 0, -1, 2, 2, 1, 0, -2, 2, 3, -1, 1, 0, -2, 3, 4, 0, -1, 2, 0, -3, 4, 5, 1, 0, -2, 2, 0, -4, 5, 7, -1, 1, 0, -2, 3, 0, -5, 7, 9, 0, -1, 2, 0, -3, 4, 0, -7, 9, 12, 1, 0, -2, 2, 0, -4, 5, 0, -9, 12, 16, -1, 1, 0, -2, 3, 0, -5, 7, 0, -12, 16, 21
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OFFSET
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6,6
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COMMENTS
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Right border = Padovan sequence starting with offset 6.
Row sums = Padovan sequence starting with offset 7.
Sum of n-th row terms = rightmost term of next row.
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LINKS
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Table of n, a(n) for n=6..83.
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FORMULA
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Triangle read by rows, T(n,k) = M * (A000931 * 0^(n-k)). M = an infinite lower triangular matrix with A106510 in every column: (1, 1, -1, 0, 1, -1, 0, 1, -1,...); and A000931 is a diagonalized infinite lower triangular matrix with the Padovan sequence starting with offset 6: (1, 1, 2, 2, 3, 4, 5, 7, 9,...) as the main diagonal and the rest zeros.
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EXAMPLE
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First few rows of the triangle =
1;
1, 1;
-1, 1, 2;
0, -1, 2, 2;
1, 0, -2, 2, 3;
-1, 1, 0, -2, 3, 4;
0, -1, 2, 0, -3, 4, 5;
1, 0, -2, 2, 0, -4, 5, 7;
-1, 1, 0, -2, 3, 0, -5, 7, 9;
0, -1, 2, 0, -3, 4, 0, -7, 9, 12;
1, 0, -2, 2, 0, -4, 5, 0, -9, 12, 16;
...
Example: Row 10 = (1, 0, -2, 2, 3) with A000931(10) = 3, rightmost term. This row = the termwise products of ((1, 0, -1, 1, 1) and (1, 1, 2, 2, 3); where the Padovan sequence starting with offset 6 = (1, 1, 2, 2, 3, 4, 5, 7, 9,...).
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CROSSREFS
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A000931, A106510
Sequence in context: A110249 A160756 A176239 * A159934 A067460 A159855
Adjacent sequences: A145459 A145460 A145461 * A145463 A145464 A145465
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KEYWORD
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eigen,tabl,sign
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AUTHOR
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Gary W. Adamson, Oct 10 2008
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STATUS
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approved
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