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A216208
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a(1) = 11. a(n) is obtained by filling the space between neighboring entries by the sum of the first two entries of a(n-1).
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1
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OFFSET
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1,1
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COMMENTS
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Definition of "entry": Call each digit of a(1) and each inserted sum an entry.
(1) Philosophy. Sequence expresses the nesting pattern of hierarchical higher-order vagueness (formal description in Bobzien 2013, 17-20; informal description e.g. in Shapiro 2005, 147-8) (2) Biology. At least the first five numbers of the sequence are manifested in various biological structures, so in vessel arrangement in Microcosmus helleri; in the pereional appendages of Augustidontus seriatus, in the rip structure (“Berippung”) of pecten (velopecten) Vewzprimiensis Bittn.(formal description in Salson 2010, 115).
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REFERENCES
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S. Bobzien, Higher-order vagueness and borderline nestings - a persistent confusion, Analytic Philosophy 54 (2013), 1-49.
M. Salson, Structures d'indexation compressées et dynamiques pour le texte (doctoral dissertation, bioinformatics) Université de Rouen 2010.
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LINKS
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Table of n, a(n) for n=1..7.
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FORMULA
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a(1) = 11. a(n) is obtained by filling the space between neighboring entries by the sum of the first two entries of a(n-1).
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EXAMPLE
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a(2) = 121; for a(3), in 1-2-1 the two (-) are replaced by 1+2 = 3 hence a(3) = 13231.
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MATHEMATICA
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a[1]="11"; a[n_] := a[n] = StringInsert[a[n-1], ToString@n, 1 + Range[2^(n-1)]]; Table[a[n], {n, 9}] (* Giovanni Resta, Mar 12 2013 *)
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CROSSREFS
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Sequence in context: A080486 A342233 A082776 * A110398 A176595 A067218
Adjacent sequences: A216205 A216206 A216207 * A216209 A216210 A216211
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KEYWORD
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base,easy,nonn
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AUTHOR
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Susanne Bobzien, Mar 12 2013
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STATUS
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approved
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