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A004280
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2 together with the odd numbers (essentially the result of the first stage of the sieve of Eratosthenes).
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24
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1, 2, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29, 31, 33, 35, 37, 39, 41, 43, 45, 47, 49, 51, 53, 55, 57, 59, 61, 63, 65, 67, 69, 71, 73, 75, 77, 79, 81, 83, 85, 87, 89, 91, 93, 95, 97, 99, 101, 103, 105, 107, 109, 111, 113, 115, 117, 119, 121, 123, 125, 127, 129, 131
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OFFSET
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1,2
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COMMENTS
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Number of Fibonacci binary words of length n and having no subword 1011. A Fibonacci binary word is a binary word having no 00 subword. Example: a(5) = 9 because of the 13 Fibonacci binary words of length 5 the following do not qualify: 11011, 10110, 10111 and 01011. - Emeric Deutsch, May 13 2007
a(1) = 1; for n > 1, a(n) = least number > a(n-1) which is a unique sum of two earlier terms, not necessarily distinct. - Franklin T. Adams-Watters, Nov 01 2011
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REFERENCES
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F. S. Roberts, Applied Combinatorics, Prentice-Hall, 1984, p. 256.
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LINKS
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FORMULA
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G.f.: x*(1+x^3)/(1-x)^2;
a(n) = 2*n - 3 + C(1, n-1) + C(0, n-1). (End)
E.g.f.: (1/2)*(6 + 4*x + x^2 - 2*(3 - 2*x)*exp(x)). - G. C. Greubel, Nov 25 2021
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MAPLE
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MATHEMATICA
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PROG
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(Sage) [1, 2]+[2*n-3 for n in (3..70)] # G. C. Greubel, Nov 25 2021
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CROSSREFS
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KEYWORD
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easy,nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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