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Search: id:A072705
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| A072705 |
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Triangle of number of unimodal partitions/compositions of n into exactly k distinct terms. |
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+0
3
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| 1, 1, 0, 1, 2, 0, 1, 2, 0, 0, 1, 4, 0, 0, 0, 1, 4, 4, 0, 0, 0, 1, 6, 4, 0, 0, 0, 0, 1, 6, 8, 0, 0, 0, 0, 0, 1, 8, 12, 0, 0, 0, 0, 0, 0, 1, 8, 16, 8, 0, 0, 0, 0, 0, 0, 1, 10, 20, 8, 0, 0, 0, 0, 0, 0, 0, 1, 10, 28, 16, 0, 0, 0, 0, 0, 0, 0, 0, 1, 12, 32, 24, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 12, 40, 40, 0, 0
(list; table; graph; listen)
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OFFSET
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1,5
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FORMULA
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T(n, k) =2^(k-1)*A060016(n, k) =T(n-k, k)+2*T(n-k, k-1) [starting with T(0, 0)=0, T(0, 1)=0 and T(n, 1)=1 for n>0]
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EXAMPLE
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Rows start: 1; 1,0; 1,2,0; 1,2,0,0; 1,4,0,0,0; 1,4,4,0,0,0; 1,6,4,0,0,0,0; 1,6,8,0,0,0,0,0; etc. T(6,3)=4 since 6 can be written as 1+2+3, 1+3+2, 2+3+1, or 3+2+1 but not 2+1+3 or 3+1+2.
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CROSSREFS
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Cf. A060016, A072574, A072704. Row sums are A072706.
Sequence in context: A085496 A101661 A079644 this_sequence A072574 A058650 A112177
Adjacent sequences: A072702 A072703 A072704 this_sequence A072706 A072707 A072708
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KEYWORD
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nonn,tabl
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AUTHOR
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Henry Bottomley (se16(AT)btinternet.com), Jul 04 2002
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