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A071676
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Array read by antidiagonals of signed variant of trinomial coefficients with T(n,k)=T(n-1,k)+T(n-1,k-1)-T(n-1,k-2) starting with T(0,0)=1.
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1
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1, 0, 1, 0, 1, 1, 0, -1, 2, 1, 0, 0, -1, 3, 1, 0, 0, -2, 0, 4, 1, 0, 0, 1, -5, 2, 5, 1, 0, 0, 0, 0, -8, 5, 6, 1, 0, 0, 0, 3, -5, -10, 9, 7, 1, 0, 0, 0, -1, 8, -15, -10, 14, 8, 1, 0, 0, 0, 0, 2, 11, -30, -7, 20, 9, 1, 0, 0, 0, 0, -4, 15, 6, -49, 0, 27, 10, 1, 0, 0, 0, 0, 1, -10, 41, -14, -70, 12, 35, 11, 1, 0, 0, 0, 0, 0, -5, -6, 77, -56, -90, 30, 44
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OFFSET
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0,9
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COMMENTS
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Each column is eventually positive, i.e. for each k there is a number j(k) such that T(n,k) is positive for all n>=j(k). Despite this, each row sum is 1.
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LINKS
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EXAMPLE
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Rows start:
1, 0, 0, 0, 0, ...;
1, 1, -1, 0, 0, 0, ...;
1, 2, -1, -2, 1, 0, 0, ...;
1, 3, 0, -5, 0, 3, -1, 0, ...;
1, 4, 2, -8, -5, 8, 2, -4, 1, ...;
etc...
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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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