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Search: id:A059618
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| A059618 |
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Number of strongly unimodal partitions of n (strongly unimodal means strictly increasing then strictly decreasing). |
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+0
4
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| 1, 1, 1, 3, 4, 6, 10, 15, 21, 30, 43, 59, 82, 111, 148, 199, 263, 344, 451, 584, 751, 965, 1230, 1560, 1973, 2483, 3110, 3885, 4834, 5990, 7405, 9123, 11202, 13724, 16762, 20417, 24815, 30081, 36377, 43900, 52860, 63511, 76166, 91157, 108886, 129842
(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) =A059619(n, 0) =sum_k[A059619(n, k)] for k>0 when n>0.
G.f.: 1+Sum_{k>=0} (x^(k+1)*Product_{i=1..k} (1+x^i)^2). - Vladeta Jovovic (vladeta(AT)eunet.rs), Dec 05 2003
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EXAMPLE
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a(6)=10 since 6 can be written as 6, 5+1, 4+2, 3+2+1, 2+4, 2+3+1, 1+5, 1+4+1, 1+3+2 or 1+2+3 (but for example neither 2+2+1+1 nor 1+2+2+1 which are only weakly unimodal).
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CROSSREFS
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Cf. A000009, A000041, A001523, A059607, A059619.
Adjacent sequences: A059615 A059616 A059617 this_sequence A059619 A059620 A059621
Sequence in context: A074321 A085378 A125869 this_sequence A114736 A099417 A139463
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KEYWORD
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nice,nonn
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AUTHOR
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Henry Bottomley (se16(AT)btinternet.com), Jan 31 2001
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