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A342708
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Triangle read by rows with n >= 1, 0 <= k <= n-1: in general T(n,k) = T(n-1,k-1) - T(n-k,k), except T(1,0)=1, T(n,0)=0 for n>=2; T(n,k) = 0 for k>=n.
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1
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1, 0, 1, 0, -1, 1, 0, 1, -1, 1, 0, -1, 0, -1, 1, 0, 1, 0, 0, -1, 1, 0, -1, 1, -1, 0, -1, 1, 0, 1, -1, 2, -1, 0, -1, 1, 0, -1, 0, -1, 1, -1, 0, -1, 1, 0, 1, 0, 1, 0, 1, -1, 0, -1, 1, 0, -1, 1, -2, 1, -1, 1, -1, 0, -1, 1, 0, 1, -1, 2, -1, 2, -1, 1, -1, 0, -1, 1
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OFFSET
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1,32
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COMMENTS
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Absolute value of sum of triangle array rows = A000700.
Sum of absolute value of each number in a row = absolute value of A000025.
Triangle recurrence is the same as A008284 (row sums equal A000041) except instead of adding the two pieces for the corresponding output a subtraction is performed.
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LINKS
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EXAMPLE
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The triangle begins:
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n\k| 0 1 2 3 4 5 6 7 8 9 10 11 ...
---+--------------------------------------------------
1 | 1;
2 | 0, 1;
3 | 0, -1, 1;
4 | 0, 1, -1, 1;
5 | 0, -1, 0, -1, 1;
6 | 0, 1, 0, 0, -1, 1;
7 | 0, -1, 1, -1, 0, -1, 1;
8 | 0, 1, -1, 2, -1, 0, -1, 1;
9 | 0, -1, 0, -1, 1, -1, 0, -1, 1;
10 | 0, 1, 0, 1, 0, 1, -1, 0, -1, 1;
11 | 0, -1, 1, -2, 1, -1, 1, -1, 0, -1, 1;
12 | 0, 1, -1, 2, -1, 2, -1, 1, -1, 0, -1, 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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