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
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).
Jorma K. Merikoski, Pentti Haukkanen, and Timo Tossavainen, The congruence x^n = -a^n (mod m): Solvability and related OEIS sequences, Notes. Num. Theor. Disc. Math. (2024) Vol. 30, No. 3, 516-529. See p. 528.
H. B. Meyer, Eratosthenes' sieve
Index entries for linear recurrences with constant coefficients, signature (2,-1).
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
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