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A125513
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a(n) is the number of binary strings of length n such that no subsequence of length 5 or less contains 4 or more ones.
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1
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2, 4, 8, 15, 26, 48, 89, 165, 305, 561, 1034, 1908, 3521, 6496, 11982, 22101, 40770, 75210, 138741, 255934, 472117, 870911, 1606567, 2963628, 5466988, 10084919, 18603592, 34317946, 63306130, 116780470, 215424285, 397391986, 733066807
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,1
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FORMULA
| a(n) = a(n-1) + a(n-2) + a(n-4) + 2a(n-5) - a(n-7) - a(n-10).
G.f.: x*(2+2*x+2*x^2+3*x^3+x^4-x^5-x^6-x^7-x^8-x^9)/(1-x-x^2-x^4-2*x^5+x^7+x^ 10) [From Maksym Voznyy (voznyy(AT)mail.ru), Jul 26 2009]
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CROSSREFS
| This sequence is similar to the sequences A118647 (where no substring of length 4 contains 3 or more ones), because the number of ones we are checking for is one less than the length of a substring. It is also similar to A120118 (where no substring of length 5 contains 3 or more ones.).
Sequence in context: A003241 A182844 A191630 * A054174 A001523 A000126
Adjacent sequences: A125510 A125511 A125512 * A125514 A125515 A125516
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KEYWORD
| nonn
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AUTHOR
| Tanya Khovanova (tanyakh(AT)yahoo.com), Dec 28 2006
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EXTENSIONS
| G.f. proposed by Maksym Voznyy checked and corrected by R. J. Mathar, Sep 16 2009.
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