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A073463
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Triangle of number of partitions of 2n into powers of 2 where the largest part is 2^k.
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1
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1, 1, 1, 1, 2, 1, 1, 3, 2, 0, 1, 4, 4, 1, 0, 1, 5, 6, 2, 0, 0, 1, 6, 9, 4, 0, 0, 0, 1, 7, 12, 6, 0, 0, 0, 0, 1, 8, 16, 10, 1, 0, 0, 0, 0, 1, 9, 20, 14, 2, 0, 0, 0, 0, 0, 1, 10, 25, 20, 4, 0, 0, 0, 0, 0, 0, 1, 11, 30, 26, 6, 0, 0, 0, 0, 0, 0, 0, 1, 12, 36, 35, 10, 0, 0, 0, 0, 0, 0, 0, 0, 1, 13, 42, 44
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OFFSET
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0,5
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COMMENTS
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In the recurrence T(n,k)=T(n-1,k)+T([n/2],k-1): T(n-1,k) represents the partitions where the smallest part is 1 and T([n/2],k-1) those where it is not.
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LINKS
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FORMULA
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T(n, k) = T(n-1, k)+T([n/2], k-1) starting with T(n, 0)=1 and T(0, k)=0 for k>0.
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EXAMPLE
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Rows start:
1;
1, 1;
1, 2, 1;
1, 3, 2, 0;
1, 4, 4, 1, 0;
1, 5, 6, 2, 0, 0;
...
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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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