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Search: id:A115626
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| A115626 |
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Number of non-squashing partitions of {1,...,n}. |
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+0
3
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| 1, 1, 2, 4, 14, 26, 107, 190, 1234, 2182, 9947, 17414, 126953, 228398, 1039404, 1857419, 19047146, 35215110, 168364007, 307674658, 2378963269, 4429446046, 20237375204, 37371654467, 410117798653, 776233491226, 3797821367602
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OFFSET
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0,3
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COMMENT
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A "non-squashing" partition of n is one where n=p_1+p_2+...+p_k with 1 <= p_1 <= p_2 <= ... <= p_k and p_1 + p_2 + ... + p_i <= p_{i+1} for all 1 <= i < k.
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LINKS
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N. J. A. Sloane and J. A. Sellers, On non-squashing partitions, Discrete Math., 294 (2005), 259-274.
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FORMULA
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a(n) = SUM {i = 0 to ceiling(n/2)-1} (binomial(n, i)*a(i)) + [if n is even] binomial(n, n/2)*(a(n/2)-1/2).
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CROSSREFS
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Cf. A018819, A115625.
Sequence in context: A050564 A047830 A036051 this_sequence A116021 A095977 A129744
Adjacent sequences: A115623 A115624 A115625 this_sequence A115627 A115628 A115629
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KEYWORD
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nonn
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AUTHOR
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Christian G. Bower (bowerc(AT)usa.net), Jan 26 2006
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