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Search: id:A072706
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| A072706 |
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Number of unimodal partitions/compositions of n into distinct terms. |
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+0
5
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| 1, 1, 1, 3, 3, 5, 9, 11, 15, 21, 33, 39, 55, 69, 93, 127, 159, 201, 261, 327, 411, 537, 653, 819, 1011, 1257, 1529, 1899, 2331, 2829, 3441, 4179, 5031, 6093, 7305, 8767, 10575, 12573, 14997, 17847, 21223, 25089, 29757, 35055, 41379, 48801, 57285, 67131
(list; graph; listen)
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OFFSET
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0,4
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FORMULA
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a(n) =sum_k A072705(n, k) =A032020(n)-A072707(k)
G.f.: 1/2*(1+Product_{k>0} (1+2*x^k)). - Vladeta Jovovic (vladeta(AT)eunet.rs), Jun 24 2003
a(n) = sum_k A072705(n, k) = A032020(n)-A072707(k) = A032302(n)/2 (n>0).
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EXAMPLE
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a(6)=9 since 6 can be written as 1+2+3, 1+3+2, 1+5, 2+3+1, 2+4, 3+2+1, 4+2, 5+1, or 6, but not for example 1+4+1 (which does not have distinct terms) nor 2+1+3 (which is not unimodal).
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CROSSREFS
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Cf. A000009, A000041, A001523, A032020, A059618, A072705, A072707.
Sequence in context: A136791 A091916 A102437 this_sequence A117433 A159284 A078028
Adjacent sequences: A072703 A072704 A072705 this_sequence A072707 A072708 A072709
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KEYWORD
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nonn
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AUTHOR
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Henry Bottomley (se16(AT)btinternet.com), Jul 04 2002
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