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A004280 2 together with the odd numbers (essentially the result of the first stage of the sieve of Eratosthenes). 24
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 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,2
COMMENTS
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
REFERENCES
F. S. Roberts, Applied Combinatorics, Prentice-Hall, 1984, p. 256.
LINKS
Borys Kuca, Structures in Additive Sequences, arXiv:1804.09594 [math.NT], 2018. See V(1,2).
H. B. Meyer, Eratosthenes' sieve
FORMULA
From Paul Barry, Mar 05 2007: (Start)
G.f.: x*(1+x^3)/(1-x)^2;
a(n) = 2*n - 3 + C(1, n-1) + C(0, n-1). (End)
a(n) = 2*n - 3 + floor(2/n). - Wesley Ivan Hurt, May 23 2013
E.g.f.: (1/2)*(6 + 4*x + x^2 - 2*(3 - 2*x)*exp(x)). - G. C. Greubel, Nov 25 2021
MAPLE
1, 2, seq(2*n-1, n=2..70); # Emeric Deutsch, May 13 2007
MATHEMATICA
Union[ Join[ 2Range[70] - 1, {2}]] (* Robert G. Wilson v *)
PROG
(PARI) a(n)=2*n + 2\n - 3 \\ Charles R Greathouse IV, Nov 01 2011
(Sage) [1, 2]+[2*n-3 for n in (3..70)] # G. C. Greubel, Nov 25 2021
CROSSREFS
Cf. A002858.
Sequence in context: A338923 A360126 A004274 * A053224 A277334 A091377
KEYWORD
easy,nonn
AUTHOR
EXTENSIONS
Offset changed to 1 and formulas updated accordingly (at the suggestion of Michel Marcus) by Charles R Greathouse IV, Sep 03 2013
STATUS
approved

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Last modified March 28 05:39 EDT 2024. Contains 371235 sequences. (Running on oeis4.)