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A130194
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Let M = lower triangular matrix with 1's on and below the main diagonal, with columns multiplied by +1, +1, -1, -1, repeated; form M^2; read across rows of resulting triangle.
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1
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1, 2, 1, -1, 2, 1, -4, -1, 2, 1, 1, -4, -1, 2, 1, 6, 1, -4, -1, 2, 1, -1, 6, 1, -4, -1, 2, 1, -8, -1, 6, 1, -4, -1, 2, 1, 1, -8, -1, 6, 1, -4, -1, 2, 1, 10, 1, -8, -1, 6, 1, -4, -1, 2, 1, -1, 10, 1, -8, -1, 6, 1, -4, -1, 2, 1, -12, -1, 10, 1, -8, -1, 6, 1, -4, -1, 2, 1
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OFFSET
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1,2
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COMMENTS
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Left border = A009531: (1, 2, -1, -4, 1, 6, -1, ...).
Row sums = A130195: (1, 3, 2, -2, -1, 5, 4, ...).
Row sums of the unsigned triangle = A058074: (1, 3, 4, 8, 9, 15, ...).
A009531 in every column: (1, 2, -1, -4, 1, 6, -1, ...).
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LINKS
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EXAMPLE
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First few rows of the triangle:
1;
2, 1;
-1, 2, 1;
-4, -1, 2, 1;
1, -4, -1, 2, 1;
6, 1, -4, -1, 2, 1;
...
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PROG
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(PARI) trg(nn) = {vgf = x*(1+x)^2/(1+x^2)^2 + O(x^(nn+1)); m = matrix(nn, nn, i, j, if (i >= j, polcoeff(vgf, i-j+1))); for (n=1, nn, for (k=1, n, print1(m[n, k], ", "); ); print(); ); } \\ Michel Marcus, Oct 03 2014
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CROSSREFS
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KEYWORD
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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