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A361442
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Infinite triangle T(n, k), n, k >= 0, read and filled by rows the greedy way with distinct integers such that for any n, k >= 0, T(n, k) + T(n+1, k) + T(n+1, k+1) = 0; each term is minimal in absolute value and in case of a tie, preference is given to the positive value.
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2
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0, 1, -1, 2, -3, 4, 3, -5, 8, -12, 5, -8, 13, -21, 33, 6, -11, 19, -32, 53, -86, -2, -4, 15, -34, 66, -119, 205, 9, -7, 11, -26, 60, -126, 245, -450, 10, -19, 26, -37, 63, -123, 249, -494, 944, 7, -17, 36, -62, 99, -162, 285, -534, 1028, -1972
(list;
table;
graph;
refs;
listen;
history;
text;
internal format)
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OFFSET
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0,4
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COMMENTS
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Will every integer appear in the triangle?
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LINKS
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FORMULA
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T(n, k) = (-1)^k * Sum_{i = 0..k} binomial(k, i) * T(n-i, 0).
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EXAMPLE
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Triangle begins:
0
1 -1
2 -3 4
3 -5 8 -12
5 -8 13 -21 33
6 -11 19 -32 53 -86
-2 -4 15 -34 66 -119 205
9 -7 11 -26 60 -126 245 -450
10 -19 26 -37 63 -123 249 -494 944
7 -17 36 -62 99 -162 285 -534 1028 -1972
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PROG
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(PARI) See Links section.
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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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