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Search: id:A012257
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| A012257 |
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Table: row 1 is {1,1}; if row n is {r_1, ..., r_k} then row n+1 is {r_k 1's, r_{k-1} 2's, r_{k-2} 3's, etc.}. |
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+0
7
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| 1, 1, 1, 2, 1, 1, 2, 1, 1, 2, 3, 1, 1, 1, 2, 2, 3, 4, 1, 1, 1, 1, 2, 2, 2, 3, 3, 4, 4, 5, 6, 7, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 4, 4, 4, 4, 5, 5, 5, 5, 6, 6, 6, 7, 7, 7, 8, 8, 9, 9, 10, 10, 11, 12, 13, 14
(list; graph; listen)
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OFFSET
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1,4
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COMMENT
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The shape of each row tends to a limit curve when scaled to a fixed size. It is the same limit curve as this continuous version: start with f_0=x over [0,1]; then repeatedly reverse (1-x), integrate from zero (x-x^2/2), scale to 1 (2x-x^2), and invert (1-sqrt(1-x)). For the limit curve we have f'(0) = F(1) = lim A011784(n+2)/(A011784(n+1)*A011784(n)) ~ 0.27887706 (obtained numerically) - Martin Fuller (martin_n_fuller(AT)btinternet.com), Aug 07 2006
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FORMULA
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n-th row sum = A011784(n+2); e.g. 5-th row is {1, 1, 1, 2, 2, 3, 4} and the sum of elements is 1+1+1+2+2+3+4=14=A011784(7) - Benoit Cloitre (benoit7848c(AT)orange.fr), Aug 06 2003
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EXAMPLE
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{1,1}, {1,2}, {1,1,2}, {1,1,2,3}, {1,1,1,2,2,3,4}, {1,1,1,1,2,2,2,3,3,4,4,5,6,7}
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CROSSREFS
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Cf. A011784.
Adjacent sequences: A012254 A012255 A012256 this_sequence A012258 A012259 A012260
Sequence in context: A134024 A029316 A104368 this_sequence A101022 A051064 A078770
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KEYWORD
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nonn,tabf,nice
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AUTHOR
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Lionel Levine (levine(AT)ultranet.com)
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