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A137712
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Triangle read by rows: T(n,k) = T(n-1, k-1) - T(n-k, k-1); with left border = the Fibonacci sequence.
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1
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1, 1, 1, 2, 0, 1, 3, 1, 0, 1, 5, 1, 0, 0, 1, 8, 2, 1, 0, 0, 1, 13, 3, 1, 1, 0, 0, 1, 21, 5, 2, 1, 1, 0, 0, 1, 34, 8, 3, 2, 0, 1, 0, 0, 1, 55, 13, 5, 2, 2, 0, 1, 0, 0, 1, 89, 21, 8, 4, 2, 1, 0, 1, 0, 0, 1, 144, 34, 13, 6, 3, 2, 1, 0, 1, 0, 0, 1, 233, 55, 21, 10, 5, 3, 1, 1, 0, 1, 0, 0, 1, 377, 89, 34
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OFFSET
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1,4
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COMMENTS
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Row sums = A137713: (1, 2, 3, 5, 7, 13, 19, 31, 49, 80, 127,...). A137710 is the analogous triangle with left border = (1, 2, 4, 8, 16, 32,...).
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LINKS
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Table of n, a(n) for n=1..94.
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FORMULA
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T(n,k) = T(n-1, k-1) - T(n-k, k-1), given left border = (1, 1, 2, 3, 5, 8, 13,...).
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EXAMPLE
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First few rows of the triangle are:
1;
1, 1;
2, 0, 1;
3, 1, 0, 1;
5, 1, 0, 0, 1;
8, 2, 1, 0, 0, 1;
13, 3, 1, 1, 0, 0, 1;
21, 5, 2, 1, 1, 0, 0, 1;
34, 8, 3, 2, 0, 1, 0, 0, 1;
55, 13, 5, 2, 2, 0, 1, 0, 0, 1;
89, 21, 8, 4, 2, 1, 0, 1, 0, 0, 1;
144, 34, 13, 6, 3, 2, 1, 0, 1, 0, 0, 1;
233, 55, 21, 10, 5, 3, 1, 1, 0, 1, 0, 0, 1;
377, 89, 34, 16, 8, 4, 3, 1, 1, 0, 1, 0, 0, 1;
...
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CROSSREFS
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Cf. A137713, A137710.
Sequence in context: A079221 A168019 A026794 * A194711 A168532 A181940
Adjacent sequences: A137709 A137710 A137711 * A137713 A137714 A137715
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KEYWORD
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nonn,tabl
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AUTHOR
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Gary W. Adamson, Feb 08 2008
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STATUS
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approved
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