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A146973
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Eigentriangle, row sums = A000931 starting with offset 3.
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1
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1, -1, 1, 2, -1, 0, -2, 2, 0, 1, 3, -2, 0, -1, 1, -3, 3, 0, 2, -1, 1, 4, -3, 0, -2, 2, -1, 2, -4, 4, 0, 3, -2, 2, -2, 2, 5, -4, 0, -3, 3, -2, 4, -2, 3, -5, 5, 0, 4, -3, 3, -4, 4, -3, 4, 6, -5, 0, -4, 4, -3, 6, -4, 5, -6, 6, 0, 5, -4, 4, -6, 6, -6, 8, -5, 7
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OFFSET
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3,4
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COMMENTS
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Row sums and right border = the Padovan sequence, A000931 starting with offset 3: (1, 1, 0, 1, 1, 1, 2, 2, 3,...).
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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Triangle read by rows, T * Q, where T = an infinite lower triangular matrix with (1, -1, 2, -2, 3, -3,...) in every column and Q = an infinite lower triangular matrix with the Padovan sequence, A000931 as the main diagonal starting with offset 3: (1, 1, 0, 1, 1, 1, 2, 2, 3,...). The rest of triangle Q = all zeros. This triangle = T * Q.
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EXAMPLE
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First few rows of the triangle =
1;
-1, 1;
2, -1, 0;
-2, 2, 0, 1;
3, -2, 0, -1, 1;
-3, 3, 0, 2, -1, 1;
4, -3, 0, -2, 2, -1, 2;
-4, 4, 0, 3, -2, 2, -2, 2;
5, -4, 0, -3, 3, -2, 4, -2, 3;
-5, 5, 0, 4, -3, 3, -4, 4, -3, 4;
6, -5, 0, -4, 4, -3, 6, -4, 6, -4, 5;
-6, 6, 0, 5, -4, 4, -6, 6, -6, 8, -5, 7;
7, -6, 0, -5, 5, -4, 8, -6, 9, -8, 10, -7, 9
-7, 7, 0, 6, -5, 5, -8, 8, -9, 12, -10, 14, -9, 12;
...
Row 6 = (-2, 2, 0, 1) = termwise products of (-2, 2, 0, 1) and (1, 1, 0, 1).
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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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