

A004280


2 together with the odd numbers (essentially the result of the first stage of the sieve of Eratosthenes).


23



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

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(n1) which is a unique sum of two earlier terms, not necessarily distinct.  Franklin T. AdamsWatters, Nov 01 2011


REFERENCES

F. S. Roberts, Applied Combinatorics, PrenticeHall, 1984, p. 256.


LINKS

G. C. Greubel, Table of n, a(n) for n = 1..5000
Borys Kuca, Structures in Additive Sequences, arXiv:1804.09594 [math.NT], 2018. See V(1,2).
H. B. Meyer, Eratosthenes' sieve
Index entries for linear recurrences with constant coefficients, signature (2,1).
Index entries for sequences generated by sieves


FORMULA

From Paul Barry, Mar 05 2007: (Start)
G.f.: x*(1+x^3)/(1x)^2;
a(n) = 2*n  3 + C(1, n1) + C(0, n1). (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*n1, 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*n3 for n in (3..70)] # G. C. Greubel, Nov 25 2021


CROSSREFS

Cf. A002858.
Sequence in context: A355330 A338923 A004274 * A053224 A277334 A091377
Adjacent sequences: A004277 A004278 A004279 * A004281 A004282 A004283


KEYWORD

easy,nonn


AUTHOR

N. J. A. Sloane


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



