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Search: id:A008747
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| A008747 |
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Expansion of (1+x^4)/((1-x)*(1-x^2)*(1-x^3)). |
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+0
2
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| 1, 1, 2, 3, 5, 6, 9, 11, 14, 17, 21, 24, 29, 33, 38, 43, 49, 54, 61, 67, 74, 81, 89, 96, 105, 113, 122, 131, 141, 150, 161, 171, 182, 193, 205, 216, 229, 241, 254, 267, 281, 294, 309, 323, 338, 353, 369, 384, 401, 417, 434, 451, 469, 486, 505
(list; graph; listen)
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OFFSET
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0,3
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COMMENT
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"In standard bootstrap percolation, a subset A of the n x n grid is initially infected. A new site is then infected if at least two of its neighbours are infected and an infected site stays infected forever. The set A is said to percolate if eventually the entire grid is infected. A percolating set is said to be minimal if none of its subsets percolate. Answering a question of Bollobas, we show that there exists a minimal percolating set of size 4n^2/33 + o(n^2), but there does not exist one larger than (n + 2)^2/6." - Jonathan Vos Post (jvospost3(AT)gmail.com), Feb 13 2007
For n>=1, the set {A008747(6n+-1)} is the set of numbers of the form a^2+5(a+1)^2 for -inf < a < inf. Furthermore the set A008747(6n) is A033581(n). - Kieren MacMillan (kieren(AT)alumni.rice.edu), Dec 19 2007
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LINKS
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Robert Morris, Minimal percolating sets in bootstrap percolation, 13 Feb 2007.
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FORMULA
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Ceiling(n^2/6).
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CROSSREFS
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Cf. A033581.
Sequence in context: A046657 A102825 A070991 this_sequence A054639 A070757 A123399
Adjacent sequences: A008744 A008745 A008746 this_sequence A008748 A008749 A008750
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KEYWORD
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nonn
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AUTHOR
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N. J. A. Sloane (njas(AT)research.att.com).
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