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A004280 2 together with the odd numbers (essentially the result of the first stage of the sieve of Eratosthenes). 21
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

Table of n, a(n) for n=1..67.

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

G.f.: x(1+x^3)/(1-x)^2; a(n) = 2n - 3 + C(1, n-1) + C(0, n-1). - Paul Barry, Mar 05 2007

a(n) = 2*n - 3 + floor(2/n). - Wesley Ivan Hurt, May 23 2013

MAPLE

1, 2, seq(2*n-1, n=2..66); # Emeric Deutsch, May 13 2007

MATHEMATICA

Union[ Join[ 2Range[65] - 1, {2}]] (* Robert G. Wilson v *)

PROG

(PARI) a(n)=2*n + 2\n - 3 \\ Charles R Greathouse IV, Nov 01 2011

CROSSREFS

Cf. A002858.

Sequence in context: A186330 A153809 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

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Last modified October 17 00:03 EDT 2019. Contains 328103 sequences. (Running on oeis4.)