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Search: id:A135473
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| A135473 |
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a(n) = number of strings of length n that can be obtained by starting with abc and repeatedly doubling any substring in place. |
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+0
16
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| 0, 0, 1, 3, 8, 21, 54, 138, 355, 924, 2432, 6461, 17301, 46657, 126656, 345972, 950611, 2626253, 7292268, 20342805, 56993909, 160317859, 452642235, 1282466920, 3645564511, 10395117584, 29727982740, 85251828792, 245120276345, 706529708510, 2041260301955, 5910531770835, 17149854645474, 49859456251401, 145223624492108, 423722038708874, 1238318400527185
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OFFSET
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1,4
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COMMENT
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Several generalizations suggest themselves: What if we start with k different letters (here k=3)? What if we start with k different letters and fix the number of duplications d? See A137739, A137740, A137741, A137742, A137743, A137744, A137745, A137746, A137747, A137748.
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LINKS
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Index entries for doubling substrings
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FORMULA
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Empirically, grows like 3^n.
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EXAMPLE
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n=3: abc
n=4: aabc, abbc, abcc
n=5: aaabc, abbbc, abccc, aabbc, aabcc, abbcc, ababc, abcbc
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CROSSREFS
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Cf. A135017, A135156, A135157, A135475, A135479, A130838.
Cf. also A137739, A137740, A137741, A137742, A137743, A137744, A137745, A137746, A137747, A137748.
Sequence in context: A094723 A127358 A077849 this_sequence A005580 A027932 A084625
Adjacent sequences: A135470 A135471 A135472 this_sequence A135474 A135475 A135476
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KEYWORD
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nonn
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AUTHOR
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Max Alekseyev (maxal(AT)cs.ucsd.edu), Jan 07 2008
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EXTENSIONS
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a(19) - a(33) from David Applegate, Feb 12 2008
Extended to 37 terms by David Applegate, Feb 16 2008
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