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Search: id:A073463
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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
(list; table; graph; listen)
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OFFSET
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0,5
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COMMENT
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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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H. Bottomley, Illustration of initial terms
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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; etc.
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CROSSREFS
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Columns include A000012, A000027, A002620, A008804. Subsequent columns start like A000123 (offset). Row sums are A000123.
Sequence in context: A003687 A104575 A046223 this_sequence A127948 A145975 A026792
Adjacent sequences: A073460 A073461 A073462 this_sequence A073464 A073465 A073466
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KEYWORD
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easy,nonn,tabl
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AUTHOR
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Henry Bottomley (se16(AT)btinternet.com), Aug 02 2002
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